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2026-10-03T06:25:58Z
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https://www.mathepedia.wiki/w/index.php?title=Homeomorphism&diff=248
Homeomorphism
2026-08-22T04:27:01Z
<p>InfernalAtom683: </p>
<hr />
<div>{{Topology banner}}<br />
[[File:Topology joke.jpg|thumb|250x250px|A homeomorphism that turns a coffee mug into a donut continuously.]]<br />
A '''homeomorphism''' is a special type of [[function]] between two [[Topological space|topological spaces]], that establishes that the two spaces are fundamentally the same from a topological perspective. Specifically, it is a [[Continuous function|continuous]] [[bijective]] function whose [[inverse function]] is also continuous. Homeomorphisms are the [[Isomorphism|isomorphisms]] in the [[category of topological spaces]] <math>\mathsf{Top}</math>, which preserves all [[topological properties]] of a topological space. If such a function exists between two spaces, they are said to be '''homeomorphic'''. <br />
<br />
Intuitively, two spaces are homeomorphic if one can be continuously deformed into the other by stretching, bending, and twisting, without cutting, tearing, or gluing. A typical intuitive example is that a mug with a handle is homeomorphic to a donut. This concept is distinct from [[Homotopy#Homotopy equivalence|homotopy equivalence]], which allows deformations that involve collapsing. For instance, a solid ball can be continuously shrunk to a point by a homotopy, but such a deformation is not a homeomorphism because it is not bijective and the inverse would not be continuous.<br />
<br />
== Definitions ==<br />
A function <math>f</math> between topological spaces <math>X</math> and <math>Y</math> is called a '''homeomorphism''', if:<br />
<br />
* <math>f</math> is continuous,<br />
* <math>f</math> is bijective,<br />
* <math>f^{-1}</math> is continuous.<br />
<br />
Two topological spaces <math>X</math> and <math>Y</math> are called '''homeomorphic''' if there exists a homeomorphism between them, denoted <math>X\cong Y</math>.<br />
<br />
=== Equivalent Definitions ===<br />
A homeomorphism is a bijection that is continuous and [[Open function|open]], or continuous and [[Closed function|closed]].<br />
<br />
== Properties ==<br />
{{Property|property=The composition of two homeomorphisms is again a homeomorphism.}}<br />
{{Proof|proof=Let <math>f\colon X \to Y</math> and <math>g\colon Y \to Z</math> be homeomorphisms. Then:<br />
<br />
* <math>g \circ f\colon X \to Z</math> is bijective, since the composition of two bijections is a bijection.<br />
<br />
* <math>g \circ f</math> is continuous, as the composition of two continuous functions.<br />
<br />
* The inverse is <math>(g \circ f)^{-1} = f^{-1} \circ g^{-1}</math>, which is continuous because it is the composition of the continuous functions <math>g^{-1}</math> and <math>f^{-1}</math>.<br />
<br />
Thus <math>g \circ f</math> satisfies all requirements of a homeomorphism.}}<br />
<br />
<br />
{{Property|property=The inverse of a homeomorphism is again a homeomorphism.}}<br />
{{Proof|proof=Let <math>f\colon X \to Y</math> be a homeomorphism. Then:<br />
* <math>f^{-1}</math> is continuous by definition,<br />
* <math>f^{-1}</math> is bijective, since the inverse of a bijection is again a bijection,<br />
* <math>\left(f^{-1}\right)^{-1}=f</math> is continuous by definition.}}<br />
<br />
<br />
{{Property|property=Homeomorphism is an [[equivalence relation]].}}<br />
<br />
{{Proof|proof=<br />
* '''Reflexivity''': The identity map <math>\operatorname{id}_X\colon X\to X</math> is a continuous bijection on any topological space <math>X</math>, whose inverse is itself. Thus <math>\operatorname{id}_X</math> is a homeomorphism.<br />
* '''Symmetry''': If <math>f\colon X\to Y</math> is a homeomorphism, then its inverse <math>f^{-1}\colon Y\to X</math> is again a homeomorphism.<br />
* '''Transitivity''': If <math>f\colon X\to Y</math> and <math>g\colon Y\to Z</math> are homeomorphisms, then <math>g\circ f: X\to Z</math> is again a homeomorphism.<br />
}}<br />
<br />
== Examples ==<br />
<br />
=== Open interval ===<br />
The [[open interval]] <math>(0,1)</math> is homeomorphic to <math>\mathbb{R}</math>.<br />
{{Proof|proof=The map <math>f\colon (0,1)\to \mathbb{R}</math> defined by<br />
<math display="block">f(x)=\tan\left(\pi\left(x-\dfrac12\right)\right)</math><br />
is a homeomorphism. Indeed, <math>f</math> is continuous because it is a composition of continuous functions. The restriction <math>\tan\colon (-\pi/2,\pi/2)\to\mathbb{R}</math> is bijective with continuous inverse <math>\arctan\colon \mathbb{R}\to(-\pi/2,\pi/2)</math>. Therefore <math>f</math> is bijective and its inverse<br />
<math display="block">f^{-1}(y)=\dfrac1\pi\arctan(y)+\dfrac12</math><br />
is continuous. Thus <math>f</math> is a homeomorphism.}}<br />
<br />
=== Stereographic projection ===<br />
The [[Euclidean plane]] <math>\mathbb{R}^2</math> is homeomorphic to the [[2-sphere]] minus one point, denoted <math>S^2 \setminus \{N\}</math> where <math>N=(0,0,1)</math> is the [[north pole]].<br />
<br />
{{Proof|proof=<br />
<div style="float:right; width:320px; margin:0 0 0.5em 1em;"><br />
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<br />
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</tikz><br />
</div><br />
Define the [[stereographic projection]] <math>p\colon S^2 \setminus \{N\} \to \mathbb{R}^2</math> by<br />
<math display="block">p(x,y,z) = \left( \frac{x}{1-z}, \frac{y}{1-z} \right).</math><br />
This map is continuous because it is a rational function with denominator nonzero (since <math>z<1</math> on <math>S^2\setminus\{N\}</math>).<br />
<br />
The inverse map <math>p^{-1}\colon \mathbb{R}^2 \to S^2 \setminus \{N\}</math> is given by<br />
<math display="block">p^{-1}(u,v) = \left( \frac{2u}{u^2+v^2+1}, \frac{2v}{u^2+v^2+1}, \frac{u^2+v^2-1}{u^2+v^2+1} \right).</math><br />
This is also continuous as a composition of continuous functions. One verifies that <math>p \circ p^{-1} = \text{id}_{\mathbb{R}^2}</math> and <math>p^{-1} \circ p = \operatorname{id}_{S^2\setminus\{N\}}</math> by direct substitution. Hence <math>p</math> is a homeomorphism.<br />
}}<br />
<br />
=== Quotient space ===<br />
The unit interval <math>[0,1]</math> with the endpoints identified (the quotient space <math>[0,1]/\sim</math> where <math>0\sim 1</math>) is homeomorphic to the circle <math>S^1</math>.<br />
<br />
{{Proof|proof=Define the map <math>f\colon [0,1] \to S^1</math> by <math display="block">f(t)=(\cos(2\pi t), \sin(2\pi t)).</math> This map is continuous and [[Surjection|surjective]], and satisfies <math>f(0)=f(1)=(1,0)</math>.<br />
<br />
Consider the equivalence relation <math>\sim</math>, and let <math>q\colon [0,1]\to [0,1]/\sim</math> be the [[quotient map]]. By the [[universal property]] of the quotient map, there exists a unique continuous map <math>\tilde{f}\colon [0,1]/\sim \to S^1</math> such that <math>\tilde{f} \circ q = f</math>; that is, the following diagram commutes:<br />
<div style="text-align: center;"><br />
<cd><br />
{[0,1]} && {S^1} \\<br />
& {[0,1]/{\sim}} \arrow["f", from=1-1, to=1-3]<br />
\arrow["q"', from=1-1, to=2-2]<br />
\arrow["{\exists! \tilde{f}}"', dashed, from=2-2, to=1-3]<br />
</cd><br />
</div><br />
<br />
The map <math>\tilde{f}</math> is bijective because:<br />
* Surjectivity follows from surjectivity of <math>f</math>;<br />
* [[Injection|Injectivity]] holds because <math display="block">\tilde{f}([t])=\tilde{f}([s])\Rightarrow t=s \text{ or } \{t,s\}=\{0,1\},</math> but in the latter case <math>[t]=[s]</math> in the quotient. <br />
<br />
Hence <math>\tilde{f}</math> is a continuous bijection.<br />
<br />
The space <math>[0,1]/\sim</math> is compact as the quotient of a [[compact space]], and <math>S^1</math> is [[Hausdorff space|Hausdorff]]. By the [[Compact-to-Hausdorff theorem]], a continuous bijection from a compact space to a Hausdorff space is a homeomorphism.<br />
<br />
Therefore <math>\tilde{f}</math> is a homeomorphism.<br />
<br />
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<br />
}}<br />
<br />
== Counterexamples ==<br />
<math>\mathbb{R}</math> is '''not''' homeomorphic to <math>\mathbb{R}^2</math>.<br />
<br />
{{Proof|proof=For contradiction, suppose that there exists a homeomorphism <math>f\colon \mathbb{R}\to\mathbb{R}^2</math>.<br />
<br />
Consider the subspace <math>\mathbb{R}\setminus\{0\}</math> of <math>\mathbb{R}</math>. The [[restriction]] on it, <math>\left.f\right|_{\mathbb{R}\setminus\{0\}}\colon \mathbb{R}\setminus\{0\}\to \mathbb{R}^2\setminus\{f(0)\}</math> is also a homeomorphism.<br />
<br />
However, <math>\mathbb{R}\setminus\{0\}</math> has two connected components, <math>(-\infty,0)</math> and <math>(0,\infty)</math>, while <math>\mathbb{R}^2\setminus\{f(0)\}</math> is connected, which contradicts the assumption that the two spaces are homeomorphic.<br />
<br />
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<br />
Hence, no such homeomorphism exists; therefore <math>\mathbb{R}</math> is not homeomorphic to <math>\mathbb{R}^2</math>}}<br />
<br />
The map from the interval <math>[0,1)</math> to the 1-sphere <math>S^1</math>,<br />
<math display="block">\phi\colon [0,1)\to S^1,\quad x\mapsto e^{2\pi ix}</math><br />
is continuous and bijective, but not a homeomorphism. <br />
{{Proof|proof=<br />
<div style="margin-left: auto; margin-right: auto; width:500px;"><br />
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<br />
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<br />
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<br />
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</div><br />
The map <math>\phi</math> is:<br />
* Continuous, as it is the composition of continuous maps <math>x\mapsto 2\pi x</math> and <math>t\mapsto e^{it}</math>.<br />
* Injective, because if <math>e^{2\pi i x_1}=e^{2\pi i x_2}</math>, then <math>x_1-x_2\in \mathbb{Z}</math>. Since <math>x_1,x_2\in [0,1)</math>, it follows that <math>x_1=x_2</math>.<br />
* Surjective, since every point of <math>S^1</math> can be written as <math>e^{2\pi i x}</math> for some <math>x\in [0,1)</math>.<br />
Hence <math>\phi</math> is a continuous bijection.<br />
<br />
However, <math>\phi</math> is not a homeomorphism.<br />
<br />
Consider the sequence<math display="block">z_n = e^{2\pi i (1-\tfrac{1}{n})} \in S^1.</math><br />
Then <math>z_n \to 1 = e^{2\pi i \cdot 0}</math> in <math>S^1</math>. But<br />
<math display="block">\phi^{-1}(z_n) = 1-\frac{1}{n} \to 1,</math><br />
which does not converge to <math>\phi^{-1}(1)=0</math> in <math>[0,1)</math>. Thus <math>\phi^{-1}</math> is not continuous.<br />
}}<br />
<br />
== Topological invariants ==<br />
A [[topological invariant]] is a property of a topological space that is preserved under homeomorphisms. In other words, if two spaces are homeomorphic, they either both possess the property or both do not. Invariants are the important tools to classify topological spaces. If two spaces differ in any topological invariant, they cannot be homeomorphic. Conversely, showing that two spaces share many invariants is often the first step on proving they are homeomorpic, though it is never sufficient by itself.<br />
<br />
=== Common topological invariants ===<br />
<br />
* [[Connectedness]]<br />
* [[Compactness]]<br />
* [[Hausdorff space|Hausdorff property]]<br />
* [[Cardinality]] of the space<br />
<br />
=== Algebraic invariants ===<br />
More powerful invariants come from [[algebraic topology]], which assigns algebraic objects to topological spaces.<br />
<br />
* [[Fundamental group]]<br />
* [[Homology group]]<br />
* [[Higher homotopy group]]<br />
<br />
==Homeomorphism group==<br />
The collection of all [[autohomeomorphisms]] of a topological space <math>X</math> forms a [[group]] under composition operation, known as the homeomorphism group of <math>X</math>, denoted <math>\operatorname{Homeo}(X)</math>. The homeomorphism group captures the symmetry in topology. It describes the ways in which a topological space can be continuously transformed onto itself.<br />
<br />
The homeomorphism group <math>\operatorname{Homeo}(X)</math> is a faithful [[group action]] on its underlying set <math>X</math>. It moves points in <math>X</math> continuously onto <math>X</math> itself, and the topological structure of <math>X</math> is also reflected in the algebraic invariants such as the [[Orbit|orbits]] and [[Stabilizer|stabilizers]] of the action.<br />
<br />
For example, consider the 2-sphere <math>S^2</math> as a thin rubber membrane tightly wraped around a ball. Each autohomeomorphism of <math>S^2</math>, which is an element in <math>\operatorname{Homeo}(S^2)</math>, corresponds to a continuous deformation of this membrane. This operation can be stretching, bending, twisting, or any composition of these operations, so the rubber always remains attached to the ball.<br />
<div style="margin-left: auto; margin-right: auto; width:500px;"><br />
<tikz width=100%><br />
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(0.7, 1.1) .. controls (1.0, 1.3) and (1.3, 1.1) .. (1.4, 0.5) <br />
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</div><br />
Under the natural action of <math>\operatorname{Homeo}(S^2)</math>, every point on the sphere can be moved continuously to any other point. This example shows how the homeomorphism group captures the symmetry of a topological space in the perspective of continuity.<br />
<br />
==See also==<br />
* [[Homotopy]]<br />
* [[Topology]]<br />
* [[Homeomorphism group]]<br />
<br />
==Terminology==<br />
{{Terminology_table|<br />
{{Terminology_table/row | homeomorphism | homéomorphisme | Homeomorphismus | 同胚 | 同胚 | 同相写像 }}<br />
{{Terminology_table/row | homeomorphic | homéomorphe | homeomorph | 同胚的 | 同胚的 | 同相 }}<br />
{{Terminology_table/row | topological invariant | invariant topologique | topologische Invariante | 拓扑不变量 | 拓撲不變量 | 位相不変量 }}<br />
{{Terminology_table/row | autohomeomorphism | autohoméomorphisme | Selbsthomöomorphismus | 自同胚 | 自同胚 | 自己同相写像 }}<br />
{{Terminology_table/row | homeomorphism group | groupe des homéomorphismes | Homöomorphismengruppe | 同胚群 | 同胚群 | 同相群 }}<br />
}}<br />
<br />
[[Category:Topology]]</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Statement/styles.css&diff=247
Template:Statement/styles.css
2026-07-17T10:56:41Z
<p>InfernalAtom683: </p>
<hr />
<div>.global-box.math-statement {<br />
border-left-width: 0.25em;<br />
border-radius: 0;<br />
}<br />
<br />
.global-box.math-statement--proof {<br />
border-left-color: #36c;<br />
}<br />
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border-left-color: #14866d;<br />
}<br />
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border-left-color: #7256a8;<br />
}<br />
<br />
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border-left-color: #ac6600;<br />
}<br />
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border-left-color: #b32424;<br />
}<br />
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border-left-color: #72777d;<br />
}<br />
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font-size: 1em;<br />
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}<br />
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}<br />
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flex: 1 1 auto;<br />
min-width: 0;<br />
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line-height: 1.4;<br />
}<br />
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@media (max-width: 500px) {<br />
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padding-left: 0.5em;<br />
}<br />
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.math-statement.compact-note .global-box__body {<br />
padding-right: 0.5em;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:CompactNote&diff=246
Template:CompactNote
2026-07-17T10:56:04Z
<p>InfernalAtom683: Created page with "{{Statement | type=note | title={{{title|Note}}} | content={{{note|{{{1|}}}}}} | style={{{style|}}} | class=compact-note {{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=note<br />
| title={{{title|Note}}}<br />
| content={{{note|{{{1|}}}}}}<br />
| style={{{style|}}}<br />
| class=compact-note {{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Mathepedia:Terminology_submissions&diff=245
Mathepedia:Terminology submissions
2026-07-16T18:24:02Z
<p>InfernalAtom683: New terminology translation: Hausdorff space (Ελληνικά)</p>
<hr />
<div>== Translation: Hausdorff space — Ελληνικά ==<br />
<br />
* '''Source page:''' [[Hausdorff space]]<br />
* '''Term:''' <nowiki>Hausdorff space</nowiki><br />
* '''Language:''' <nowiki>Ελληνικά</nowiki><br />
* '''Translation:''' <nowiki>χώρος Χάουσντορφ</nowiki><br />
* '''Submitted by:''' [[User:InfernalAtom683|InfernalAtom683]] ([[User talk:InfernalAtom683|talk]]) 02:19, 17 July 2026 (CST)</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=MediaWiki:Common.js&diff=244
MediaWiki:Common.js
2026-07-16T18:19:25Z
<p>InfernalAtom683: Created page with "/* Any JavaScript here will be loaded for all users on every page load. */ ( function ( mw, $ ) { 'use strict'; var submissionPage = 'Project:Terminology submissions'; var otherValue = '__other__'; var languages = [ 'English', 'Français', 'Deutsch', '日本語', '中文', 'Español', 'Italiano', 'Português', 'Ελληνικά', 'Русский', '한국어', 'العربية', 'हिन्दी', 'Bahasa Indonesia', 'Nederlands',..."</p>
<hr />
<div>/* Any JavaScript here will be loaded for all users on every page load. */<br />
<br />
( function ( mw, $ ) {<br />
'use strict';<br />
<br />
var submissionPage = 'Project:Terminology submissions';<br />
var otherValue = '__other__';<br />
var languages = [<br />
'English',<br />
'Français',<br />
'Deutsch',<br />
'日本語',<br />
'中文',<br />
'Español',<br />
'Italiano',<br />
'Português',<br />
'Ελληνικά',<br />
'Русский',<br />
'한국어',<br />
'العربية',<br />
'हिन्दी',<br />
'Bahasa Indonesia',<br />
'Nederlands',<br />
'Polski',<br />
'Türkçe',<br />
'Українська',<br />
'Tiếng Việt',<br />
'ไทย'<br />
];<br />
<br />
function wrapNowiki( value ) {<br />
return '<nowiki>' + String( value ).replace( /<\/nowiki\s*>/gi, '&lt;/nowiki&gt;' ) + '</nowiki>';<br />
}<br />
<br />
function setStatus( form, message, type ) {<br />
var status = form.querySelector( '.terminology-form-status' );<br />
status.className = 'terminology-form-status' +<br />
( type ? ' terminology-form-status--' + type : '' );<br />
status.textContent = message;<br />
}<br />
<br />
function option( value, label, disabled, selected ) {<br />
var item = document.createElement( 'option' );<br />
item.value = value;<br />
item.textContent = label;<br />
item.disabled = !!disabled;<br />
item.selected = !!selected;<br />
return item;<br />
}<br />
<br />
function initialiseForm( form ) {<br />
var controls, languageSelect, otherLanguage, translation, submit, term;<br />
<br />
if ( form.getAttribute( 'data-terminology-ready' ) === 'yes' ) {<br />
return;<br />
}<br />
form.setAttribute( 'data-terminology-ready', 'yes' );<br />
<br />
term = form.querySelector( '.terminology-form-term' ).textContent.trim();<br />
controls = form.querySelector( '.terminology-form-controls' );<br />
controls.textContent = '';<br />
<br />
languageSelect = document.createElement( 'select' );<br />
languageSelect.className = 'terminology-language-select';<br />
languageSelect.setAttribute( 'aria-label', 'Language' );<br />
languageSelect.appendChild( option( '', 'Choose language', true, true ) );<br />
languages.forEach( function ( language ) {<br />
languageSelect.appendChild( option( language, language ) );<br />
} );<br />
languageSelect.appendChild( option( otherValue, 'Other language…' ) );<br />
<br />
otherLanguage = document.createElement( 'input' );<br />
otherLanguage.type = 'text';<br />
otherLanguage.className = 'terminology-other-language';<br />
otherLanguage.placeholder = 'Language name';<br />
otherLanguage.setAttribute( 'aria-label', 'Other language name' );<br />
otherLanguage.hidden = true;<br />
<br />
translation = document.createElement( 'input' );<br />
translation.type = 'text';<br />
translation.className = 'terminology-translation-input';<br />
translation.placeholder = 'Enter translation';<br />
translation.setAttribute( 'aria-label', 'Translation' );<br />
<br />
submit = document.createElement( 'button' );<br />
submit.type = 'button';<br />
submit.className = 'terminology-translation-submit';<br />
submit.textContent = 'Submit translation';<br />
<br />
controls.appendChild( languageSelect );<br />
controls.appendChild( otherLanguage );<br />
controls.appendChild( translation );<br />
controls.appendChild( submit );<br />
<br />
languageSelect.addEventListener( 'change', function () {<br />
otherLanguage.hidden = languageSelect.value !== otherValue;<br />
if ( !otherLanguage.hidden ) {<br />
otherLanguage.focus();<br />
}<br />
} );<br />
<br />
submit.addEventListener( 'click', function () {<br />
var language = languageSelect.value === otherValue ?<br />
otherLanguage.value.trim() : languageSelect.value;<br />
var translatedTerm = translation.value.trim();<br />
var sourcePage = String( mw.config.get( 'wgPageName' ) || '' ).replace( /_/g, ' ' );<br />
var sectionTitle;<br />
var sectionText;<br />
<br />
if ( !language ) {<br />
setStatus( form, 'Please choose or enter a language.', 'error' );<br />
languageSelect.focus();<br />
return;<br />
}<br />
if ( !translatedTerm ) {<br />
setStatus( form, 'Please enter a translation.', 'error' );<br />
translation.focus();<br />
return;<br />
}<br />
<br />
sectionTitle = 'Translation: ' + term + ' — ' + language;<br />
sectionText =<br />
"* '''Source page:''' [[" + sourcePage + "]]\n" +<br />
"* '''Term:''' " + wrapNowiki( term ) + "\n" +<br />
"* '''Language:''' " + wrapNowiki( language ) + "\n" +<br />
"* '''Translation:''' " + wrapNowiki( translatedTerm ) + "\n" +<br />
"* '''Submitted by:''' [[User:InfernalAtom683|InfernalAtom683]] ([[User talk:InfernalAtom683|talk]]) 02:19, 17 July 2026 (CST)";<br />
<br />
submit.disabled = true;<br />
setStatus( form, 'Submitting…' );<br />
<br />
new mw.Api().postWithToken( 'csrf', {<br />
action: 'edit',<br />
title: submissionPage,<br />
section: 'new',<br />
sectiontitle: sectionTitle,<br />
text: sectionText,<br />
summary: ( 'New terminology translation: ' + term + ' (' + language + ')' ).slice( 0, 240 ),<br />
watchlist: 'nochange',<br />
formatversion: 2<br />
} ).done( function () {<br />
translation.value = '';<br />
setStatus( form, 'Translation submitted for review. Thank you!', 'success' );<br />
} ).fail( function ( code, data ) {<br />
var detail = data && data.error && data.error.info ? ' ' + data.error.info : '';<br />
setStatus( form, 'Submission failed.' + detail, 'error' );<br />
} ).always( function () {<br />
submit.disabled = false;<br />
} );<br />
} );<br />
}<br />
<br />
function initialiseTerminologyForms( $content ) {<br />
$content.find( '.terminology-translation-form' ).each( function () {<br />
initialiseForm( this );<br />
} );<br />
}<br />
<br />
mw.loader.using( 'mediawiki.api' ).then( function () {<br />
mw.hook( 'wikipage.content' ).add( initialiseTerminologyForms );<br />
} );<br />
}( mediaWiki, jQuery ) );</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=243
Template:Terminology/styles.css
2026-07-16T18:18:21Z
<p>InfernalAtom683: </p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.45em 0 0.8em;<br />
color: #202122;<br />
font-size: 0.875rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 0.7em;<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid #c8ccd1;<br />
background: #fff;<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header {<br />
display: grid;<br />
grid-template-columns: 19% 17% 19% 13% 17% 15%;<br />
min-height: 42px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid #c8ccd1;<br />
}<br />
<br />
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border-top: 1px solid #c8ccd1;<br />
border-spacing: 0;<br />
border-collapse: collapse;<br />
table-layout: fixed;<br />
background: transparent;<br />
}<br />
<br />
.terminology-cell--english { width: 19%; }<br />
.terminology-cell--french { width: 17%; }<br />
.terminology-cell--german { width: 19%; }<br />
.terminology-cell--japanese { width: 13%; }<br />
.terminology-cell--chinese { width: 17%; }<br />
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<br />
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height: 42px;<br />
}<br />
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box-sizing: border-box;<br />
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vertical-align: middle;<br />
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overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row > .terminology-cell,<br />
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background: #eaf3ff;<br />
}<br />
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white-space: nowrap;<br />
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background: #f8f9fa;<br />
}<br />
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.terminology-cell--more > .mw-collapsible-toggle:focus {<br />
outline: 2px solid #36c;<br />
outline-offset: -2px;<br />
}<br />
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InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=242
Template:Terminology/row
2026-07-16T18:17:47Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
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<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
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<tr class="terminology-more-row"><br />
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One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/empty&diff=241
Template:Terminology/empty
2026-07-16T18:16:51Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><div class="terminology-empty-state"><br />
<div class="terminology-empty-message">No additional translations are available yet.</div><br />
<div class="terminology-submit-title">Submit a translation in your language</div><br />
<div class="terminology-submit-help">Choose a language, enter the translated term, and submit it for review.</div><br />
<div class="terminology-translation-form"><br />
<span class="terminology-form-term">{{{term|}}}</span><br />
<div class="terminology-form-controls"><span class="terminology-form-fallback">The translation form requires the Terminology site script.</span></div><br />
<div class="terminology-form-status" role="status" aria-live="polite"></div><br />
</div><br />
</div></includeonly><noinclude><br />
Empty-state and translation-submission container used by [[Template:Terminology/row]]. The interactive language selector and translation field are created by the Terminology code installed in <code>MediaWiki:Common.js</code>.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Hausdorff_space&diff=240
Hausdorff space
2026-07-16T15:26:18Z
<p>InfernalAtom683: </p>
<hr />
<div>{{Topology banner<br />
| breadcrumb = {{Breadcrumb nav|[[Mathepedia]]|[[Topology]]|[[General topology]]|[[Hausdorff space]]}}<br />
}}<br />
A '''Hausdorff space''' (or '''<math>T_2</math> space''') is a type of [[topological space]] in which points can be "cleanly separated" by neighborhoods. Specifically, for any two distinct points, there exist disjoint [[Open set|open sets]] containing each point. Consequently, Hausdorff property ensures that limits of sequences are unique when they exist.<br />
<br />
== Definitions ==<br />
{{Definition|<br />
A topological space <math>(X,\tau)</math> is Hausdorff, if for any two points <math>x,y\in X</math>, there exists two disjoint open sets <math>U,V\in \tau</math>, <math>U\cap V=\varnothing</math>, such that <math>x\in U</math> and <math>y\in V</math>.<br />
}}<br />
=== Equivalent Definitions ===<br />
Any convergent [[sequence]] in <math>X</math> has at most one limit.<br />
<br />
== Properties ==<br />
{{Property<br />
|property=Subspaces of Hausdorff spaces are Hausdorff.<br />
|proof=Let <math>Y \subseteq X</math> with <math>X</math> Hausdorff. For <math>y_1, y_2 \in Y, y_1 \neq y_2</math>, there exist disjoint open sets <math>U, V \subseteq X</math> with <math>y_1 \in U</math> and <math>y_2 \in V</math>. Then <math>U \cap Y</math> and <math>V \cap Y</math> are disjoint open sets in <math>Y</math> containing <math>y_1</math> and <math>y_2</math>.<br />
}}<br />
<br />
{{Property<br />
|property=Finite products of Hausdorff spaces are Hausdorff.<br />
|proof=Let <math>X_1, \dots, X_n</math> be Hausdorff. Consider points <math>(x_1, \dots, x_n) \neq (y_1, \dots, y_n)</math>. There exists an index <math>i</math> with <math>x_i \neq y_i</math>.<br />
<br />
Since <math>X_i</math> is Hausdorff, choose disjoint open sets <math>U_i, V_i \subseteq X_i</math> containing <math>x_i</math> and <math>y_i</math>. Then <math>U_1 \times \dots \times U_n</math> and <math>V_1 \times \dots \times V_n</math> are disjoint open sets containing the two points.}}<br />
<br />
{{Property<br />
|property=Compact subsets of Hausdorff spaces are closed.<br />
|proof=Let <math>K \subseteq X</math> be compact and <math>X</math> Hausdorff. For any <math>x \in X \setminus K</math>, for each <math>y \in K</math> choose disjoint open sets <math>U_y\ni x</math> and <math>V_y \ni y</math>. <br />
<br />
The collection <math>\{V_y \mid y \in K\}</math> covers <math>K</math>. By compactness, finitely many <math>V_{y_1}, \dots, V_{y_n}</math> cover <math>K</math>. Then <math display="block">U = \bigcap_{i=1}^n U_{y_i}</math> is open, contains <math>x</math>, and is disjoint from <math>K</math>. Hence <math>K</math> is closed.<br />
}}<br />
<br />
== Examples ==<br />
{{Example<br />
|example=Every [[metric space]] is a Hausdorff space.<br />
|proof=<div style="float:right; width:320px; margin:0 0 0.5em 1em;"><br />
<tikz><br />
\def\r{1.5}<br />
<br />
\coordinate (x) at (0,0);<br />
<br />
\def\ang{20}<br />
<br />
\coordinate (y) at ({2*\r*cos(\ang)}, {2*\r*sin(\ang)});<br />
<br />
\draw[fill=blue!25!cyan, opacity=0.2, dashed, thick] (x) circle (\r);<br />
\draw[fill=blue!25!cyan, opacity=0.2, dashed, thick] (y) circle (\r);<br />
<br />
\fill (x) circle (2pt);<br />
\fill (y) circle (2pt);<br />
<br />
\node[below left] at (x) {$x$};<br />
\node[above right] at (y) {$y$};<br />
<br />
\draw[black, dashed, thick]<br />
(x) -- ({\r*cos(\ang)}, {\r*sin(\ang)})<br />
node[midway, above, sloped] {\footnotesize $r=\dfrac{d(x,y)}{2}$};<br />
<br />
</tikz><br />
</div><br />
Let <math>(X,d)</math> be a metric space, take two distinct points <math>x,y</math> such that <math>d(x,y)>0</math>.<br />
<br />
Consider open balls <math>B(x,r)</math> and <math>B(y,r)</math>where <math>r=\frac{d(x,y)}{2}>0</math>. The open balls are both open with <math>x\in B(x,r)</math> and <math>y\in B(y,r)</math>.<br />
<br />
For contradiction, assume there exists <math>z\in B(x,r)\cap B(y,r)</math>, then <math>d(x,z)<r</math> and <math>d(y,z)<r</math>. By triangular inequality, <math display="block">d(x,y)\leq d(x,y)+d(x,z)<r+r=d(x,y),</math> there exists a contradiction.<br />
<br />
Thus, <math>B(x,r)\cap B(y,r)=\varnothing</math>; therefore <math>(X,d)</math> is Hausdorff.<br />
}}<br />
<br />
== See also ==<br />
<br />
* [[Topological space]]<br />
* [[Convergence]]<br />
<br />
{{Terminology<br />
|rows=<br />
{{Terminology/row<br />
|english=Hausdorff space<br />
|french=espace de Hausdorff<br />
|german=hausdorff-Raum<br />
|japanese=ハウスドルフ空間<br />
|chinese=Hausdorff 空间 · Hausdorff 空間<br />
|highlight=yes<br />
}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Hausdorff_space&diff=239
Hausdorff space
2026-07-16T15:25:41Z
<p>InfernalAtom683: </p>
<hr />
<div>{{Topology banner<br />
| breadcrumb = {{Breadcrumb nav|[[Mathepedia]]|[[Topology]]|[[General topology]]|[[Hausdorff space]]}}<br />
}}<br />
A '''Hausdorff space''' (or '''<math>T_2</math> space''') is a type of [[topological space]] in which points can be "cleanly separated" by neighborhoods. Specifically, for any two distinct points, there exist disjoint [[Open set|open sets]] containing each point. Consequently, Hausdorff property ensures that limits of sequences are unique when they exist.<br />
<br />
== Definitions ==<br />
{{Definition|<br />
A topological space <math>(X,\tau)</math> is Hausdorff, if for any two points <math>x,y\in X</math>, there exists two disjoint open sets <math>U,V\in \tau</math>, <math>U\cap V=\varnothing</math>, such that <math>x\in U</math> and <math>y\in V</math>.<br />
}}<br />
=== Equivalent Definitions ===<br />
Any convergent [[sequence]] in <math>X</math> has at most one limit.<br />
<br />
== Properties ==<br />
{{Property<br />
|property=Subspaces of Hausdorff spaces are Hausdorff.<br />
|proof=Let <math>Y \subseteq X</math> with <math>X</math> Hausdorff. For <math>y_1, y_2 \in Y, y_1 \neq y_2</math>, there exist disjoint open sets <math>U, V \subseteq X</math> with <math>y_1 \in U</math> and <math>y_2 \in V</math>. Then <math>U \cap Y</math> and <math>V \cap Y</math> are disjoint open sets in <math>Y</math> containing <math>y_1</math> and <math>y_2</math>.<br />
}}<br />
<br />
{{Property<br />
|property=Finite products of Hausdorff spaces are Hausdorff.<br />
|proof=Let <math>X_1, \dots, X_n</math> be Hausdorff. Consider points <math>(x_1, \dots, x_n) \neq (y_1, \dots, y_n)</math>. There exists an index <math>i</math> with <math>x_i \neq y_i</math>.<br />
<br />
Since <math>X_i</math> is Hausdorff, choose disjoint open sets <math>U_i, V_i \subseteq X_i</math> containing <math>x_i</math> and <math>y_i</math>. Then <math>U_1 \times \dots \times U_n</math> and <math>V_1 \times \dots \times V_n</math> are disjoint open sets containing the two points.}}<br />
<br />
{{Property<br />
|property=Compact subsets of Hausdorff spaces are closed.<br />
|proof=Let <math>K \subseteq X</math> be compact and <math>X</math> Hausdorff. For any <math>x \in X \setminus K</math>, for each <math>y \in K</math> choose disjoint open sets <math>U_y\ni x</math> and <math>V_y \ni y</math>. <br />
<br />
The collection <math>\{V_y \mid y \in K\}</math> covers <math>K</math>. By compactness, finitely many <math>V_{y_1}, \dots, V_{y_n}</math> cover <math>K</math>. Then <math display="block">U = \bigcap_{i=1}^n U_{y_i}</math> is open, contains <math>x</math>, and is disjoint from <math>K</math>. Hence <math>K</math> is closed.<br />
}}<br />
<br />
== Examples ==<br />
{{Example<br />
|example=Every [[metric space]] is a Hausdorff space.<br />
|proof=<div style="float:right; width:320px; margin:0 0 0.5em 1em;"><br />
<tikz><br />
\def\r{1.5}<br />
<br />
\coordinate (x) at (0,0);<br />
<br />
\def\ang{20}<br />
<br />
\coordinate (y) at ({2*\r*cos(\ang)}, {2*\r*sin(\ang)});<br />
<br />
\draw[fill=blue!25!cyan, opacity=0.2, dashed, thick] (x) circle (\r);<br />
\draw[fill=blue!25!cyan, opacity=0.2, dashed, thick] (y) circle (\r);<br />
<br />
\fill (x) circle (2pt);<br />
\fill (y) circle (2pt);<br />
<br />
\node[below left] at (x) {$x$};<br />
\node[above right] at (y) {$y$};<br />
<br />
\draw[black, dashed, thick]<br />
(x) -- ({\r*cos(\ang)}, {\r*sin(\ang)})<br />
node[midway, above, sloped] {\footnotesize $r=\dfrac{d(x,y)}{2}$};<br />
<br />
</tikz><br />
</div><br />
Let <math>(X,d)</math> be a metric space, take two distinct points <math>x,y</math> such that <math>d(x,y)>0</math>.<br />
<br />
Consider open balls <math>B(x,r)</math> and <math>B(y,r)</math>where <math>r=\frac{d(x,y)}{2}>0</math>. The open balls are both open with <math>x\in B(x,r)</math> and <math>y\in B(y,r)</math>.<br />
<br />
For contradiction, assume there exists <math>z\in B(x,r)\cap B(y,r)</math>, then <math>d(x,z)<r</math> and <math>d(y,z)<r</math>. By triangular inequality, <math display="block">d(x,y)\leq d(x,y)+d(x,z)<r+r=d(x,y),</math> there exists a contradiction.<br />
<br />
Thus, <math>B(x,r)\cap B(y,r)=\varnothing</math>; therefore <math>(X,d)</math> is Hausdorff.<br />
}}<br />
<br />
== See also ==<br />
<br />
* [[Topological space]]<br />
* [[Convergence]]<br />
<br />
==Terminology==<br />
{{Terminology_table|<br />
{{Terminology_table/row | Hausdorff space | espace de Hausdorff (espace séparé) | hausdorff-Raum (hausdorffscher Raum) | Hausdorff 空间 | Hausdorff 空間 | ハウスドルフ空間 }}<br />
}}<br />
{{Terminology<br />
|rows=<br />
{{Terminology/row<br />
|english=Hausdorff space<br />
|french=espace de Hausdorff<br />
|german=hausdorff-Raum<br />
|japanese=ハウスドルフ空間<br />
|chinese=Hausdorff 空间 · Hausdorff 空間<br />
|highlight=yes<br />
}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/empty&diff=238
Template:Terminology/empty
2026-07-16T14:53:44Z
<p>InfernalAtom683: Created page with "<includeonly><div class="terminology-empty-state"> <div class="terminology-empty-message">No additional translations are available yet.</div> <div class="terminology-submit-title">Submit a translation in your language</div> <div class="terminology-submit-help">Enter the language and translated term below. Your submission will be opened for review.</div> <div class="terminology-submit-form"><inputbox> type=commenttitle page=Project:Terminology submissions width=36 break=n..."</p>
<hr />
<div><includeonly><div class="terminology-empty-state"><br />
<div class="terminology-empty-message">No additional translations are available yet.</div><br />
<div class="terminology-submit-title">Submit a translation in your language</div><br />
<div class="terminology-submit-help">Enter the language and translated term below. Your submission will be opened for review.</div><br />
<div class="terminology-submit-form"><inputbox><br />
type=commenttitle<br />
page=Project:Terminology submissions<br />
width=36<br />
break=no<br />
placeholder=Language — translation<br />
buttonlabel=Submit translation<br />
</inputbox></div><br />
</div></includeonly><noinclude><br />
Empty-state and translation-submission form used by [[Template:Terminology/row]]. Change the <code>page=</code> value above if submissions should go to a different Wiki page. Requires Extension:InputBox.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=237
Template:Terminology/styles.css
2026-07-16T14:53:13Z
<p>InfernalAtom683: </p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.45em 0 0.8em;<br />
color: #202122;<br />
font-size: 0.875rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 0.7em;<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid #c8ccd1;<br />
border-radius: 3px;<br />
background: #fff;<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header {<br />
display: grid;<br />
grid-template-columns: 19% 17% 19% 13% 17% 15%;<br />
min-height: 42px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid #c8ccd1;<br />
}<br />
<br />
/* Each item is a real table so MediaWiki places its native toggle in the last cell. */<br />
.terminology-row {<br />
width: 100%;<br />
margin: 0;<br />
border: 0;<br />
border-top: 1px solid #c8ccd1;<br />
border-spacing: 0;<br />
border-collapse: collapse;<br />
table-layout: fixed;<br />
background: transparent;<br />
}<br />
<br />
.terminology-cell--english { width: 19%; }<br />
.terminology-cell--french { width: 17%; }<br />
.terminology-cell--german { width: 19%; }<br />
.terminology-cell--japanese { width: 13%; }<br />
.terminology-cell--chinese { width: 17%; }<br />
.terminology-cell--more { width: 15%; }<br />
<br />
.terminology-main-row {<br />
height: 42px;<br />
}<br />
<br />
.terminology-cell {<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
vertical-align: middle;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row > .terminology-cell,<br />
.terminology-row[data-highlight="yes"] .terminology-more-cell {<br />
background: #eaf3ff;<br />
}<br />
<br />
.terminology-cell--english {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-cell--more {<br />
padding: 0;<br />
border-left: 1px solid #c8ccd1;<br />
}<br />
<br />
.terminology-cell--more > .terminology-language-count {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
padding: 0.5rem 0.65rem;<br />
color: #36c;<br />
line-height: 1.3;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-row.mw-collapsible .terminology-language-count {<br />
display: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle {<br />
display: flex;<br />
float: none;<br />
align-items: center;<br />
justify-content: space-between;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
margin: 0;<br />
padding: 0.5rem 0.65rem;<br />
border: 0;<br />
border-radius: 0;<br />
background: transparent;<br />
color: #36c;<br />
font: inherit;<br />
line-height: 1.3;<br />
text-align: left;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:hover {<br />
background: #f8f9fa;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:focus {<br />
outline: 2px solid #36c;<br />
outline-offset: -2px;<br />
}<br />
<br />
.terminology-cell--more .mw-collapsible-text {<br />
color: inherit;<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::before {<br />
content: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::after {<br />
content: "";<br />
flex: 0 0 auto;<br />
box-sizing: border-box;<br />
width: 0.5rem;<br />
height: 0.5rem;<br />
margin-left: 0.55rem;<br />
border-right: 2px solid currentcolor;<br />
border-bottom: 2px solid currentcolor;<br />
transform: rotate(45deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-expanded::after {<br />
transform: rotate(225deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-more-cell {<br />
padding: 0.5rem 0.75rem 0.65rem;<br />
border-top: 0;<br />
}<br />
<br />
.terminology-extra-table {<br />
overflow: hidden;<br />
border: 1px solid #c8ccd1;<br />
border-radius: 3px;<br />
}<br />
<br />
.terminology-extra-table > p {<br />
margin: 0;<br />
}<br />
<br />
.terminology-extra-row {<br />
display: grid;<br />
grid-template-columns: 18% 32% 18% 32%;<br />
min-height: 36px;<br />
}<br />
<br />
.terminology-extra-row + .terminology-extra-row {<br />
border-top: 1px solid #c8ccd1;<br />
}<br />
<br />
.terminology-extra-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.38rem 0.7rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-extra-language {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-extra-language--second {<br />
border-left: 1px solid #c8ccd1;<br />
}<br />
<br />
.terminology-empty-state {<br />
box-sizing: border-box;<br />
padding: 0.8rem 1rem 0.9rem;<br />
}<br />
<br />
.terminology-empty-message {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-submit-title {<br />
margin-top: 0.7rem;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-submit-help {<br />
margin: 0.15rem 0 0.55rem;<br />
color: #54595d;<br />
font-size: 0.93em;<br />
}<br />
<br />
.terminology-submit-form,<br />
.terminology-submit-form form,<br />
.terminology-submit-form p {<br />
margin: 0;<br />
}<br />
<br />
.terminology-submit-form form {<br />
display: flex;<br />
align-items: center;<br />
flex-wrap: wrap;<br />
}<br />
<br />
.terminology-submit-form input[type="text"] {<br />
box-sizing: border-box;<br />
width: 24rem;<br />
max-width: 100%;<br />
height: 32px;<br />
padding: 0.35rem 0.55rem;<br />
border: 1px solid #a2a9b1;<br />
border-radius: 2px;<br />
background: #fff;<br />
color: #202122;<br />
font: inherit;<br />
}<br />
<br />
.terminology-submit-form input[type="text"]:focus {<br />
border-color: #36c;<br />
outline: 1px solid #36c;<br />
}<br />
<br />
.terminology-submit-form input[type="submit"],<br />
.terminology-submit-form button[type="submit"] {<br />
box-sizing: border-box;<br />
height: 32px;<br />
margin-left: 0.5rem;<br />
padding: 0.35rem 0.8rem;<br />
border: 1px solid #36c;<br />
border-radius: 2px;<br />
background: #36c;<br />
color: #fff;<br />
font: inherit;<br />
font-weight: 700;<br />
cursor: pointer;<br />
}<br />
<br />
.terminology-submit-form input[type="submit"]:hover,<br />
.terminology-submit-form button[type="submit"]:hover {<br />
background: #2a4b8d;<br />
}<br />
<br />
.terminology-footer {<br />
display: flex;<br />
align-items: center;<br />
min-height: 44px;<br />
box-sizing: border-box;<br />
padding: 0.3rem 0.75rem;<br />
border-top: 1px solid #c8ccd1;<br />
color: #36c;<br />
line-height: 1.3;<br />
}<br />
<br />
.terminology-footer-action {<br />
display: flex;<br />
align-items: center;<br />
}<br />
<br />
.terminology-footer-action p {<br />
display: flex;<br />
align-items: center;<br />
margin: 0;<br />
}<br />
<br />
.terminology-footer-action a {<br />
display: inline-flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-height: 32px;<br />
padding: 0 0.2rem;<br />
color: #36c;<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-footer-action a:hover {<br />
text-decoration: underline;<br />
}<br />
<br />
.terminology-footer .external {<br />
padding-right: 0;<br />
background-image: none;<br />
}<br />
<br />
.terminology-add-icon {<br />
position: relative;<br />
display: inline-block;<br />
flex: 0 0 16px;<br />
width: 16px;<br />
height: 16px;<br />
margin-right: 0.5rem;<br />
}<br />
<br />
.terminology-add-icon::before,<br />
.terminology-add-icon::after {<br />
content: "";<br />
position: absolute;<br />
border-radius: 1px;<br />
background: currentcolor;<br />
}<br />
<br />
.terminology-add-icon::before {<br />
top: 7px;<br />
left: 1px;<br />
width: 14px;<br />
height: 2px;<br />
}<br />
<br />
.terminology-add-icon::after {<br />
top: 1px;<br />
left: 7px;<br />
width: 2px;<br />
height: 14px;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: block;<br />
flex: 0 0 1px;<br />
width: 1px;<br />
height: 24px;<br />
margin: 0 0.9rem;<br />
background: #a2a9b1;<br />
}<br />
<br />
@media (max-width: 600px) {<br />
.terminology-submit-form input[type="submit"],<br />
.terminology-submit-form button[type="submit"] {<br />
margin-top: 0.45rem;<br />
margin-left: 0;<br />
}<br />
<br />
.terminology-footer {<br />
align-items: flex-start;<br />
flex-direction: column;<br />
gap: 0.55rem;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: none;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=236
Template:Terminology/row
2026-07-16T14:50:32Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages">{{#if:{{{more|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|{{{more|}}}{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}|{{Terminology/empty}}}}</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=235
Template:Terminology/row
2026-07-16T14:43:31Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=234
Template:Terminology/row
2026-07-16T14:40:48Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row{{#if:{{{more-count|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}| mw-collapsible mw-collapsed|}}" data-highlight="{{{highlight|no}}}" data-has-more="{{#if:{{{more-count|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|yes|no}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=233
Template:Terminology/row
2026-07-16T14:38:47Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row{{#if:{{{more|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}| mw-collapsible mw-collapsed|}}" data-highlight="{{{highlight|no}}}" data-has-more="{{#if:{{{more|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|yes|no}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=232
Template:Terminology/row
2026-07-16T14:38:26Z
<p>InfernalAtom683: Undo revision 231 by InfernalAtom683 (talk)</p>
<hr />
<div><includeonly><table class="terminology-row{{#if:{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}| mw-collapsible mw-collapsed|}}" data-highlight="{{{highlight|no}}}" data-has-more="{{#if:{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|yes|no}}" data-expandtext="{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages" data-collapsetext="{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Add other languages as <code>language1</code>/<code>term1</code> through <code>language12</code>/<code>term12</code>; the displayed language count is automatic.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=231
Template:Terminology/row
2026-07-16T14:37:22Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row{{#if:{{{more|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}| mw-collapsible mw-collapsed|}}" data-highlight="{{{highlight|no}}}" data-has-more="{{#if:{{{more|}}}{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|yes|no}}" data-expandtext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages" data-collapsetext="{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{{more-count|{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Numbered <code>language1</code>/<code>term1</code> parameters are counted automatically. Legacy <code>more=</code> content remains supported together with its manual <code>more-count=</code> value.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=230
Template:Terminology/styles.css
2026-07-16T14:29:47Z
<p>InfernalAtom683: </p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.45em 0 0.8em;<br />
color: var(--color-base, #202122);<br />
font-size: 0.875rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 0.7em;<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
background: var(--background-color-base, #fff);<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header {<br />
display: grid;<br />
grid-template-columns: 19% 17% 19% 13% 17% 15%;<br />
min-height: 42px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
/* Each item is a real table so MediaWiki places its native toggle in the last cell. */<br />
.terminology-row {<br />
width: 100%;<br />
margin: 0;<br />
border: 0;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-spacing: 0;<br />
border-collapse: collapse;<br />
table-layout: fixed;<br />
background: transparent;<br />
}<br />
<br />
.terminology-cell--english { width: 19%; }<br />
.terminology-cell--french { width: 17%; }<br />
.terminology-cell--german { width: 19%; }<br />
.terminology-cell--japanese { width: 13%; }<br />
.terminology-cell--chinese { width: 17%; }<br />
.terminology-cell--more { width: 15%; }<br />
<br />
.terminology-main-row {<br />
height: 42px;<br />
}<br />
<br />
.terminology-cell {<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
vertical-align: middle;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row > .terminology-cell,<br />
.terminology-row[data-highlight="yes"] .terminology-more-cell {<br />
background: var(--background-color-progressive-subtle, #eaf3ff);<br />
}<br />
<br />
.terminology-cell--english {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-cell--more {<br />
padding: 0;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-cell--more > .terminology-language-count {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
padding: 0.5rem 0.65rem;<br />
color: var(--color-progressive, #36c);<br />
line-height: 1.3;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-row.mw-collapsible .terminology-language-count {<br />
display: none;<br />
}<br />
<br />
.terminology-row[data-has-more="no"] .terminology-more-row {<br />
display: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle {<br />
display: flex;<br />
float: none;<br />
align-items: center;<br />
justify-content: space-between;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
margin: 0;<br />
padding: 0.5rem 0.65rem;<br />
border: 0;<br />
border-radius: 0;<br />
background: transparent;<br />
color: var(--color-progressive, #36c);<br />
font: inherit;<br />
line-height: 1.3;<br />
text-align: left;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:hover {<br />
background: var(--background-color-interactive-subtle, #f8f9fa);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:focus {<br />
outline: 2px solid var(--border-color-progressive--focus, #36c);<br />
outline-offset: -2px;<br />
}<br />
<br />
.terminology-cell--more .mw-collapsible-text {<br />
color: inherit;<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::before {<br />
content: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::after {<br />
content: "";<br />
flex: 0 0 auto;<br />
box-sizing: border-box;<br />
width: 0.5rem;<br />
height: 0.5rem;<br />
margin-left: 0.55rem;<br />
border-right: 2px solid currentcolor;<br />
border-bottom: 2px solid currentcolor;<br />
transform: rotate(45deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-expanded::after {<br />
transform: rotate(225deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-more-cell {<br />
padding: 0.5rem 0.75rem 0.65rem;<br />
border-top: 0;<br />
}<br />
<br />
.terminology-extra-table {<br />
overflow: hidden;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
}<br />
<br />
.terminology-extra-row {<br />
display: grid;<br />
grid-template-columns: 18% 32% 18% 32%;<br />
min-height: 36px;<br />
}<br />
<br />
.terminology-extra-row + .terminology-extra-row {<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-extra-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.38rem 0.7rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-extra-language {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-extra-language--second {<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-footer {<br />
display: flex;<br />
align-items: center;<br />
min-height: 44px;<br />
box-sizing: border-box;<br />
padding: 0.3rem 0.75rem;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
color: var(--color-progressive, #36c);<br />
line-height: 1.3;<br />
}<br />
<br />
.terminology-footer-action {<br />
display: flex;<br />
align-items: center;<br />
}<br />
<br />
.terminology-footer-action p {<br />
display: flex;<br />
align-items: center;<br />
margin: 0;<br />
}<br />
<br />
.terminology-footer-action a {<br />
display: inline-flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-height: 32px;<br />
padding: 0 0.2rem;<br />
color: var(--color-progressive, #36c);<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-footer-action a:hover {<br />
text-decoration: underline;<br />
}<br />
<br />
.terminology-footer .external {<br />
padding-right: 0;<br />
background-image: none;<br />
}<br />
<br />
.terminology-add-icon {<br />
position: relative;<br />
display: inline-block;<br />
flex: 0 0 16px;<br />
width: 16px;<br />
height: 16px;<br />
margin-right: 0.5rem;<br />
}<br />
<br />
.terminology-add-icon::before,<br />
.terminology-add-icon::after {<br />
content: "";<br />
position: absolute;<br />
border-radius: 1px;<br />
background: currentcolor;<br />
}<br />
<br />
.terminology-add-icon::before {<br />
top: 7px;<br />
left: 1px;<br />
width: 14px;<br />
height: 2px;<br />
}<br />
<br />
.terminology-add-icon::after {<br />
top: 1px;<br />
left: 7px;<br />
width: 2px;<br />
height: 14px;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: block;<br />
flex: 0 0 1px;<br />
width: 1px;<br />
height: 24px;<br />
margin: 0 0.9rem;<br />
background: var(--border-color-base, #a2a9b1);<br />
}<br />
<br />
@media (max-width: 600px) {<br />
.terminology-footer {<br />
align-items: flex-start;<br />
flex-direction: column;<br />
gap: 0.55rem;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: none;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/count&diff=229
Template:Terminology/count
2026-07-16T14:29:27Z
<p>InfernalAtom683: Created page with "<includeonly>{{#expr:{{#if:{{{1|}}}|1|0}}+{{#if:{{{2|}}}|1|0}}+{{#if:{{{3|}}}|1|0}}+{{#if:{{{4|}}}|1|0}}+{{#if:{{{5|}}}|1|0}}+{{#if:{{{6|}}}|1|0}}+{{#if:{{{7|}}}|1|0}}+{{#if:{{{8|}}}|1|0}}+{{#if:{{{9|}}}|1|0}}+{{#if:{{{10|}}}|1|0}}+{{#if:{{{11|}}}|1|0}}+{{#if:{{{12|}}}|1|0}}+{{#if:{{{13|}}}|1|0}}+{{#if:{{{14|}}}|1|0}}+{{#if:{{{15|}}}|1|0}}+{{#if:{{{16|}}}|1|0}}+{{#if:{{{17|}}}|1|0}}}}</includeonly><noinclude> Internal helper used by Template:Terminology/row to count..."</p>
<hr />
<div><includeonly>{{#expr:{{#if:{{{1|}}}|1|0}}+{{#if:{{{2|}}}|1|0}}+{{#if:{{{3|}}}|1|0}}+{{#if:{{{4|}}}|1|0}}+{{#if:{{{5|}}}|1|0}}+{{#if:{{{6|}}}|1|0}}+{{#if:{{{7|}}}|1|0}}+{{#if:{{{8|}}}|1|0}}+{{#if:{{{9|}}}|1|0}}+{{#if:{{{10|}}}|1|0}}+{{#if:{{{11|}}}|1|0}}+{{#if:{{{12|}}}|1|0}}+{{#if:{{{13|}}}|1|0}}+{{#if:{{{14|}}}|1|0}}+{{#if:{{{15|}}}|1|0}}+{{#if:{{{16|}}}|1|0}}+{{#if:{{{17|}}}|1|0}}}}</includeonly><noinclude><br />
Internal helper used by [[Template:Terminology/row]] to count non-empty language parameters.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=228
Template:Terminology/row
2026-07-16T14:29:02Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row{{#if:{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}| mw-collapsible mw-collapsed|}}" data-highlight="{{{highlight|no}}}" data-has-more="{{#if:{{{language1|}}}{{{language2|}}}{{{language3|}}}{{{language4|}}}{{{language5|}}}{{{language6|}}}{{{language7|}}}{{{language8|}}}{{{language9|}}}{{{language10|}}}{{{language11|}}}{{{language12|}}}|yes|no}}" data-expandtext="{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages" data-collapsetext="{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"><span class="terminology-language-count">{{Terminology/count|{{{english|}}}|{{{french|}}}|{{{german|}}}|{{{japanese|}}}|{{{chinese|}}}|{{{language1|}}}|{{{language2|}}}|{{{language3|}}}|{{{language4|}}}|{{{language5|}}}|{{{language6|}}}|{{{language7|}}}|{{{language8|}}}|{{{language9|}}}|{{{language10|}}}|{{{language11|}}}|{{{language12|}}}}} languages</span></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{#if:{{{language1|}}}{{{language2|}}}|{{Terminology/more row|language1={{{language1|}}}|term1={{{term1|}}}|language2={{{language2|}}}|term2={{{term2|}}}}}|}}<br />
{{#if:{{{language3|}}}{{{language4|}}}|{{Terminology/more row|language1={{{language3|}}}|term1={{{term3|}}}|language2={{{language4|}}}|term2={{{term4|}}}}}|}}<br />
{{#if:{{{language5|}}}{{{language6|}}}|{{Terminology/more row|language1={{{language5|}}}|term1={{{term5|}}}|language2={{{language6|}}}|term2={{{term6|}}}}}|}}<br />
{{#if:{{{language7|}}}{{{language8|}}}|{{Terminology/more row|language1={{{language7|}}}|term1={{{term7|}}}|language2={{{language8|}}}|term2={{{term8|}}}}}|}}<br />
{{#if:{{{language9|}}}{{{language10|}}}|{{Terminology/more row|language1={{{language9|}}}|term1={{{term9|}}}|language2={{{language10|}}}|term2={{{term10|}}}}}|}}<br />
{{#if:{{{language11|}}}{{{language12|}}}|{{Terminology/more row|language1={{{language11|}}}|term1={{{term11|}}}|language2={{{language12|}}}|term2={{{term12|}}}}}|}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Add other languages as <code>language1</code>/<code>term1</code> through <code>language12</code>/<code>term12</code>; the displayed language count is automatic.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology&diff=227
Template:Terminology
2026-07-16T14:28:35Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><templatestyles src="Terminology/styles.css" /><br />
== {{{heading|Terminology}}} ==<br />
<div class="terminology" role="region" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-intro">{{{intro|The following table lists the principal terms used in this article.}}}</div><br />
<div class="terminology-table"><br />
<div class="terminology-table-inner" role="table" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-header" role="row"><br />
<div class="terminology-header-cell" role="columnheader">{{{english-header|English}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{french-header|Français}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{german-header|Deutsch}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{japanese-header|日本語}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{chinese-header|中文}}}</div><br />
<div class="terminology-header-cell terminology-header-cell--more" role="columnheader">{{{more-header|More}}}</div><br />
</div><br />
<div class="terminology-body" role="rowgroup"><br />
{{{rows|}}}<br />
</div><br />
<div class="terminology-footer"><br />
<div class="terminology-footer-action terminology-footer-action--add">[{{{add-url|{{fullurl:{{FULLPAGENAME}}|action=edit}}}}} <span class="terminology-add-icon" aria-hidden="true"></span><span>{{{add-text|Add or verify a translation}}}</span>]</div><br />
<div class="terminology-footer-divider" aria-hidden="true"></div><br />
<div class="terminology-footer-action">[[{{{guidelines-link|Help:Terminology}}}|{{{guidelines-text|Terminology guidelines}}}]]</div><br />
</div><br />
</div><br />
</div><br />
</div></includeonly><noinclude><br />
This is the outer wrapper for the Terminology table. Supply rows through <code>rows=</code> using [[Template:Terminology/row]].<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=226
Template:Terminology/styles.css
2026-07-16T13:52:08Z
<p>InfernalAtom683: </p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.45em 0 0.8em;<br />
color: var(--color-base, #202122);<br />
font-size: 0.875rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 0.7em;<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
background: var(--background-color-base, #fff);<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header {<br />
display: grid;<br />
grid-template-columns: 19% 17% 19% 13% 17% 15%;<br />
min-height: 42px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
/* Each item is a real table so MediaWiki places its native toggle in the last cell. */<br />
.terminology-row {<br />
width: 100%;<br />
margin: 0;<br />
border: 0;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-spacing: 0;<br />
border-collapse: collapse;<br />
table-layout: fixed;<br />
background: transparent;<br />
}<br />
<br />
.terminology-cell--english { width: 19%; }<br />
.terminology-cell--french { width: 17%; }<br />
.terminology-cell--german { width: 19%; }<br />
.terminology-cell--japanese { width: 13%; }<br />
.terminology-cell--chinese { width: 17%; }<br />
.terminology-cell--more { width: 15%; }<br />
<br />
.terminology-main-row {<br />
height: 42px;<br />
}<br />
<br />
.terminology-cell {<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
vertical-align: middle;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row > .terminology-cell {<br />
background: var(--background-color-progressive-subtle, #eaf3ff);<br />
}<br />
<br />
.terminology-cell--english {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-cell--more {<br />
padding: 0;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle {<br />
display: flex;<br />
float: none;<br />
align-items: center;<br />
justify-content: space-between;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
margin: 0;<br />
padding: 0.5rem 0.65rem;<br />
border: 0;<br />
border-radius: 0;<br />
background: transparent;<br />
color: var(--color-progressive, #36c);<br />
font: inherit;<br />
line-height: 1.3;<br />
text-align: left;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:hover {<br />
background: var(--background-color-interactive-subtle, #f8f9fa);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:focus {<br />
outline: 2px solid var(--border-color-progressive--focus, #36c);<br />
outline-offset: -2px;<br />
}<br />
<br />
.terminology-cell--more .mw-collapsible-text {<br />
color: inherit;<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::before {<br />
content: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::after {<br />
content: "";<br />
flex: 0 0 auto;<br />
box-sizing: border-box;<br />
width: 0.5rem;<br />
height: 0.5rem;<br />
margin-left: 0.55rem;<br />
border-right: 2px solid currentcolor;<br />
border-bottom: 2px solid currentcolor;<br />
transform: rotate(45deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-expanded::after {<br />
transform: rotate(225deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-more-cell {<br />
padding: 0.5rem 0.75rem 0.65rem;<br />
border-top: 0;<br />
}<br />
<br />
.terminology-extra-table {<br />
overflow: hidden;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
}<br />
<br />
.terminology-extra-row {<br />
display: grid;<br />
grid-template-columns: 18% 32% 18% 32%;<br />
min-height: 36px;<br />
}<br />
<br />
.terminology-extra-row + .terminology-extra-row {<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-extra-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.38rem 0.7rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-extra-language {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-extra-language--second {<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-footer {<br />
display: flex;<br />
align-items: center;<br />
min-height: 50px;<br />
box-sizing: border-box;<br />
padding: 0.65rem 1rem;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
color: var(--color-progressive, #36c);<br />
line-height: 1.3;<br />
}<br />
<br />
.terminology-footer-action,<br />
.terminology-footer-action a {<br />
display: inline-flex;<br />
align-items: center;<br />
color: var(--color-progressive, #36c);<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-footer-action a:hover {<br />
text-decoration: underline;<br />
}<br />
<br />
.terminology-footer .external {<br />
padding-right: 0;<br />
background-image: none;<br />
}<br />
<br />
.terminology-plus {<br />
display: inline-block;<br />
margin-right: 0.5rem;<br />
font-size: 1.6rem;<br />
font-weight: 300;<br />
line-height: 0.7;<br />
transform: translateY(-1px);<br />
}<br />
<br />
.terminology-footer-divider {<br />
align-self: stretch;<br />
width: 1px;<br />
max-height: 22px;<br />
margin: 0 1.2rem;<br />
background: var(--border-color-base, #a2a9b1);<br />
}<br />
<br />
@media (max-width: 600px) {<br />
.terminology-footer {<br />
align-items: flex-start;<br />
flex-direction: column;<br />
gap: 0.55rem;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: none;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=225
Template:Terminology/row
2026-07-16T13:51:58Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-label|{{{more-count|0}}} languages}}}" data-collapsetext="{{{more-label|{{{more-count|0}}} languages}}}"><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell terminology-cell--french" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell terminology-cell--german" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell terminology-cell--japanese" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell terminology-cell--chinese" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Every row is collapsed on initial page load.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=224
Template:Terminology/styles.css
2026-07-16T13:49:32Z
<p>InfernalAtom683: </p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.45em 0 0.8em;<br />
color: var(--color-base, #202122);<br />
font-size: 0.875rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 0.7em;<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
background: var(--background-color-base, #fff);<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header {<br />
display: grid;<br />
grid-template-columns: 19% 17% 19% 13% 17% 15%;<br />
min-height: 42px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
/* Each item is a real table so MediaWiki places its native toggle in the last cell. */<br />
.terminology-row {<br />
width: 100%;<br />
margin: 0;<br />
border: 0;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-spacing: 0;<br />
border-collapse: collapse;<br />
table-layout: fixed;<br />
background: transparent;<br />
}<br />
<br />
.terminology-col--english { width: 19%; }<br />
.terminology-col--french { width: 17%; }<br />
.terminology-col--german { width: 19%; }<br />
.terminology-col--japanese { width: 13%; }<br />
.terminology-col--chinese { width: 17%; }<br />
.terminology-col--more { width: 15%; }<br />
<br />
.terminology-main-row {<br />
height: 42px;<br />
}<br />
<br />
.terminology-cell {<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.5rem 0.75rem;<br />
vertical-align: middle;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row > .terminology-cell {<br />
background: var(--background-color-progressive-subtle, #eaf3ff);<br />
}<br />
<br />
.terminology-cell--english {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-cell--more {<br />
padding: 0;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle {<br />
display: flex;<br />
float: none;<br />
align-items: center;<br />
justify-content: space-between;<br />
box-sizing: border-box;<br />
width: 100%;<br />
min-height: 42px;<br />
margin: 0;<br />
padding: 0.5rem 0.65rem;<br />
border: 0;<br />
border-radius: 0;<br />
background: transparent;<br />
color: var(--color-progressive, #36c);<br />
font: inherit;<br />
line-height: 1.3;<br />
text-align: left;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:hover {<br />
background: var(--background-color-interactive-subtle, #f8f9fa);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle:focus {<br />
outline: 2px solid var(--border-color-progressive--focus, #36c);<br />
outline-offset: -2px;<br />
}<br />
<br />
.terminology-cell--more .mw-collapsible-text {<br />
color: inherit;<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::before {<br />
content: none;<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-default::after {<br />
content: "";<br />
flex: 0 0 auto;<br />
box-sizing: border-box;<br />
width: 0.5rem;<br />
height: 0.5rem;<br />
margin-left: 0.55rem;<br />
border-right: 2px solid currentcolor;<br />
border-bottom: 2px solid currentcolor;<br />
transform: rotate(45deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-cell--more > .mw-collapsible-toggle-expanded::after {<br />
transform: rotate(225deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-more-cell {<br />
padding: 0.5rem 0.75rem 0.65rem;<br />
border-top: 0;<br />
}<br />
<br />
.terminology-extra-table {<br />
overflow: hidden;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
}<br />
<br />
.terminology-extra-row {<br />
display: grid;<br />
grid-template-columns: 18% 32% 18% 32%;<br />
min-height: 36px;<br />
}<br />
<br />
.terminology-extra-row + .terminology-extra-row {<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-extra-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.38rem 0.7rem;<br />
line-height: 1.3;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-extra-language {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-extra-language--second {<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-footer {<br />
display: flex;<br />
align-items: center;<br />
min-height: 50px;<br />
box-sizing: border-box;<br />
padding: 0.65rem 1rem;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
color: var(--color-progressive, #36c);<br />
line-height: 1.3;<br />
}<br />
<br />
.terminology-footer-action,<br />
.terminology-footer-action a {<br />
display: inline-flex;<br />
align-items: center;<br />
color: var(--color-progressive, #36c);<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-footer-action a:hover {<br />
text-decoration: underline;<br />
}<br />
<br />
.terminology-footer .external {<br />
padding-right: 0;<br />
background-image: none;<br />
}<br />
<br />
.terminology-plus {<br />
display: inline-block;<br />
margin-right: 0.5rem;<br />
font-size: 1.6rem;<br />
font-weight: 300;<br />
line-height: 0.7;<br />
transform: translateY(-1px);<br />
}<br />
<br />
.terminology-footer-divider {<br />
align-self: stretch;<br />
width: 1px;<br />
max-height: 22px;<br />
margin: 0 1.2rem;<br />
background: var(--border-color-base, #a2a9b1);<br />
}<br />
<br />
@media (max-width: 600px) {<br />
.terminology-footer {<br />
align-items: flex-start;<br />
flex-direction: column;<br />
gap: 0.55rem;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: none;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=223
Template:Terminology/row
2026-07-16T13:49:13Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><table class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-label|{{{more-count|0}}} languages}}}" data-collapsetext="{{{more-label|{{{more-count|0}}} languages}}}"><br />
<colgroup><br />
<col class="terminology-col terminology-col--english" /><br />
<col class="terminology-col terminology-col--french" /><br />
<col class="terminology-col terminology-col--german" /><br />
<col class="terminology-col terminology-col--japanese" /><br />
<col class="terminology-col terminology-col--chinese" /><br />
<col class="terminology-col terminology-col--more" /><br />
</colgroup><br />
<tr class="terminology-main-row"><br />
<td class="terminology-cell terminology-cell--english" dir="auto">{{{english|}}}</td><br />
<td class="terminology-cell" dir="auto">{{{french|}}}</td><br />
<td class="terminology-cell" dir="auto">{{{german|}}}</td><br />
<td class="terminology-cell" dir="auto">{{{japanese|}}}</td><br />
<td class="terminology-cell" dir="auto">{{{chinese|}}}</td><br />
<td class="terminology-cell terminology-cell--more"></td><br />
</tr><br />
<tr class="terminology-more-row"><br />
<td class="terminology-more-cell" colspan="6"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
</div><br />
</td><br />
</tr><br />
</table></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Every row is collapsed on initial page load.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology&diff=222
Template:Terminology
2026-07-16T13:48:53Z
<p>InfernalAtom683: </p>
<hr />
<div><includeonly><templatestyles src="Terminology/styles.css" /><br />
== {{{heading|Terminology}}} ==<br />
<div class="terminology" role="region" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-intro">{{{intro|The following table lists the principal terms used in this article.}}}</div><br />
<div class="terminology-table"><br />
<div class="terminology-table-inner" role="table" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-header" role="row"><br />
<div class="terminology-header-cell" role="columnheader">{{{english-header|English}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{french-header|Français}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{german-header|Deutsch}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{japanese-header|日本語}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{chinese-header|中文}}}</div><br />
<div class="terminology-header-cell terminology-header-cell--more" role="columnheader">{{{more-header|More}}}</div><br />
</div><br />
<div class="terminology-body" role="rowgroup"><br />
{{{rows|}}}<br />
</div><br />
<div class="terminology-footer"><br />
<span class="terminology-footer-action terminology-footer-action--add">[{{{add-url|{{fullurl:{{FULLPAGENAME}}|action=edit}}}}} <span class="terminology-plus" aria-hidden="true">+</span><span>{{{add-text|Add or verify a translation}}}</span>]</span><br />
<span class="terminology-footer-divider" aria-hidden="true"></span><br />
<span class="terminology-footer-action">[[{{{guidelines-link|Help:Terminology}}}|{{{guidelines-text|Terminology guidelines}}}]]</span><br />
</div><br />
</div><br />
</div><br />
</div></includeonly><noinclude><br />
This is the outer wrapper for the Terminology table. Supply rows through <code>rows=</code> using [[Template:Terminology/row]].<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/more_row&diff=221
Template:Terminology/more row
2026-07-16T13:35:48Z
<p>InfernalAtom683: Created page with "<includeonly><div class="terminology-extra-row" role="row"> <div class="terminology-extra-cell terminology-extra-language" role="cell" dir="auto">{{{language1|}}}</div> <div class="terminology-extra-cell" role="cell" dir="auto">{{{term1|}}}</div> <div class="terminology-extra-cell terminology-extra-language terminology-extra-language--second" role="cell" dir="auto">{{{language2|}}}</div> <div class="terminology-extra-cell" role="cell" dir="auto">{{{term2|}}}</div> </div>..."</p>
<hr />
<div><includeonly><div class="terminology-extra-row" role="row"><br />
<div class="terminology-extra-cell terminology-extra-language" role="cell" dir="auto">{{{language1|}}}</div><br />
<div class="terminology-extra-cell" role="cell" dir="auto">{{{term1|}}}</div><br />
<div class="terminology-extra-cell terminology-extra-language terminology-extra-language--second" role="cell" dir="auto">{{{language2|}}}</div><br />
<div class="terminology-extra-cell" role="cell" dir="auto">{{{term2|}}}</div><br />
</div></includeonly><noinclude><br />
One two-language row inside the expanded part of [[Template:Terminology/row]].<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/row&diff=220
Template:Terminology/row
2026-07-16T13:34:42Z
<p>InfernalAtom683: Created page with "<includeonly><div class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-label|{{{more-count|0}}} languages}}}" data-collapsetext="{{{more-label|{{{more-count|0}}} languages}}}"> <div class="terminology-main-row" role="row"> <div class="terminology-cell terminology-cell--english" role="cell" dir="auto">{{{english|}}}</div> <div class="terminology-cell" role="cell" dir="auto">{{{french|}}}</div> <div class="termino..."</p>
<hr />
<div><includeonly><div class="terminology-row mw-collapsible mw-collapsed" data-highlight="{{{highlight|no}}}" data-expandtext="{{{more-label|{{{more-count|0}}} languages}}}" data-collapsetext="{{{more-label|{{{more-count|0}}} languages}}}"><br />
<div class="terminology-main-row" role="row"><br />
<div class="terminology-cell terminology-cell--english" role="cell" dir="auto">{{{english|}}}</div><br />
<div class="terminology-cell" role="cell" dir="auto">{{{french|}}}</div><br />
<div class="terminology-cell" role="cell" dir="auto">{{{german|}}}</div><br />
<div class="terminology-cell" role="cell" dir="auto">{{{japanese|}}}</div><br />
<div class="terminology-cell" role="cell" dir="auto">{{{chinese|}}}</div><br />
<div class="terminology-cell terminology-cell--more" role="cell" aria-hidden="true"></div><br />
</div><br />
<span class="mw-collapsible-toggle-placeholder terminology-toggle-placeholder"><span class="terminology-toggle-label">{{{more-label|{{{more-count|0}}} languages}}}</span></span><br />
<div class="terminology-more-content mw-collapsible-content"><br />
<div class="terminology-extra-table" role="table" aria-label="Other languages"><br />
{{{more|}}}<br />
</div><br />
</div><br />
</div></includeonly><noinclude><br />
One terminology row. Use <code>highlight=yes</code> for the pale-blue current-page row. Every row is collapsed on initial page load.<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology&diff=219
Template:Terminology
2026-07-16T13:34:27Z
<p>InfernalAtom683: Created page with "<includeonly><templatestyles src="Terminology/styles.css" /> == {{{heading|Terminology}}} == <div class="terminology" role="region" aria-label="{{{heading|Terminology}}}"> <div class="terminology-intro">{{{intro|The following table lists the principal terms used in this article.}}}</div> <div class="terminology-table"> <div class="terminology-table-inner" role="table" aria-label="{{{heading|Terminology}}}"> <div class="terminology-header" role="row"> <div class="terminol..."</p>
<hr />
<div><includeonly><templatestyles src="Terminology/styles.css" /><br />
== {{{heading|Terminology}}} ==<br />
<div class="terminology" role="region" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-intro">{{{intro|The following table lists the principal terms used in this article.}}}</div><br />
<div class="terminology-table"><br />
<div class="terminology-table-inner" role="table" aria-label="{{{heading|Terminology}}}"><br />
<div class="terminology-header" role="row"><br />
<div class="terminology-header-cell" role="columnheader">{{{english-header|English}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{french-header|Français}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{german-header|Deutsch}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{japanese-header|日本語}}}</div><br />
<div class="terminology-header-cell" role="columnheader">{{{chinese-header|中文}}}</div><br />
<div class="terminology-header-cell terminology-header-cell--more" role="columnheader">{{{more-header|More}}}</div><br />
</div><br />
<div class="terminology-body" role="rowgroup"><br />
{{{rows|}}}<br />
</div><br />
<div class="terminology-footer"><br />
<span class="terminology-footer-action terminology-footer-action--add"><span class="terminology-plus" aria-hidden="true">+</span><span>{{{add-text|Add or verify a translation}}}</span></span><br />
<span class="terminology-footer-divider" aria-hidden="true"></span><br />
<span class="terminology-footer-action">{{{guidelines-text|Terminology guidelines}}}</span><br />
</div><br />
</div><br />
</div><br />
</div></includeonly><noinclude><br />
This is the outer wrapper for the Terminology table. Supply rows through <code>rows=</code> using [[Template:Terminology/row]].<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Terminology/styles.css&diff=218
Template:Terminology/styles.css
2026-07-16T13:33:48Z
<p>InfernalAtom683: Created page with "/* Template:Terminology/styles.css */ .terminology { margin: 0.65em 0 1em; color: var(--color-base, #202122); font-size: 1rem; } .terminology-intro { margin: 0 0 1em; line-height: 1.5; } .terminology-table { overflow-x: auto; border: 1px solid var(--border-color-subtle, #c8ccd1); border-radius: 3px; background: var(--background-color-base, #fff); } .terminology-table-inner { min-width: 760px; } .terminology-header, .terminology-main-row { display: grid; g..."</p>
<hr />
<div>/* Template:Terminology/styles.css */<br />
.terminology {<br />
margin: 0.65em 0 1em;<br />
color: var(--color-base, #202122);<br />
font-size: 1rem;<br />
}<br />
<br />
.terminology-intro {<br />
margin: 0 0 1em;<br />
line-height: 1.5;<br />
}<br />
<br />
.terminology-table {<br />
overflow-x: auto;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
background: var(--background-color-base, #fff);<br />
}<br />
<br />
.terminology-table-inner {<br />
min-width: 760px;<br />
}<br />
<br />
.terminology-header,<br />
.terminology-main-row {<br />
display: grid;<br />
grid-template-columns: 20% 18.3% 20.9% 14.1% 14.9% 11.8%;<br />
}<br />
<br />
.terminology-header {<br />
min-height: 52px;<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-header-cell,<br />
.terminology-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.72rem 2rem;<br />
line-height: 1.4;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-header-cell--more {<br />
justify-content: center;<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-row {<br />
position: relative;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-main-row {<br />
min-height: 54px;<br />
}<br />
<br />
.terminology-row[data-highlight="yes"] .terminology-main-row {<br />
background: var(--background-color-progressive-subtle, #eaf3ff);<br />
}<br />
<br />
.terminology-cell--english {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-cell--more {<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
/* The placeholder gives a stable layout before MediaWiki initialises the toggle. */<br />
.terminology-row > .terminology-toggle-placeholder,<br />
.terminology-row > .mw-collapsible-toggle {<br />
position: absolute;<br />
top: 0;<br />
right: 0;<br />
z-index: 1;<br />
display: flex;<br />
float: none;<br />
align-items: center;<br />
justify-content: space-between;<br />
box-sizing: border-box;<br />
width: 11.8%;<br />
min-height: 54px;<br />
margin: 0;<br />
padding: 0.72rem 1.25rem;<br />
border: 0;<br />
border-radius: 0;<br />
background: transparent;<br />
color: var(--color-progressive, #36c);<br />
font: inherit;<br />
line-height: 1.4;<br />
text-align: left;<br />
white-space: nowrap;<br />
}<br />
<br />
.terminology-row > .mw-collapsible-toggle {<br />
cursor: pointer;<br />
}<br />
<br />
.terminology-row > .mw-collapsible-toggle:hover {<br />
background: var(--background-color-interactive-subtle, #f8f9fa);<br />
}<br />
<br />
.terminology-row > .mw-collapsible-toggle:focus {<br />
outline: 2px solid var(--border-color-progressive--focus, #36c);<br />
outline-offset: -2px;<br />
}<br />
<br />
.terminology-row > .mw-collapsible-toggle-default::before {<br />
content: none;<br />
}<br />
<br />
.terminology-row > .terminology-toggle-placeholder::after,<br />
.terminology-row > .mw-collapsible-toggle::after {<br />
content: "";<br />
flex: 0 0 auto;<br />
box-sizing: border-box;<br />
width: 0.56rem;<br />
height: 0.56rem;<br />
margin-left: 0.75rem;<br />
border-right: 2px solid currentcolor;<br />
border-bottom: 2px solid currentcolor;<br />
transform: rotate(45deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-row > .mw-collapsible-toggle-expanded::after {<br />
transform: rotate(225deg) translate(-1px, -1px);<br />
}<br />
<br />
.terminology-row.mw-collapsed:not(.mw-made-collapsible) > .mw-collapsible-content {<br />
display: none;<br />
}<br />
<br />
.terminology-more-content {<br />
box-sizing: border-box;<br />
padding: 0.75rem 2rem 1rem;<br />
}<br />
<br />
.terminology-extra-table {<br />
overflow: hidden;<br />
border: 1px solid var(--border-color-subtle, #c8ccd1);<br />
border-radius: 3px;<br />
}<br />
<br />
.terminology-extra-row {<br />
display: grid;<br />
grid-template-columns: 18% 32% 18% 32%;<br />
min-height: 46px;<br />
}<br />
<br />
.terminology-extra-row + .terminology-extra-row {<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-extra-cell {<br />
display: flex;<br />
align-items: center;<br />
box-sizing: border-box;<br />
min-width: 0;<br />
padding: 0.55rem 1rem;<br />
line-height: 1.35;<br />
overflow-wrap: anywhere;<br />
}<br />
<br />
.terminology-extra-language {<br />
font-weight: 700;<br />
}<br />
<br />
.terminology-extra-language--second {<br />
border-left: 1px solid var(--border-color-subtle, #c8ccd1);<br />
}<br />
<br />
.terminology-footer {<br />
display: flex;<br />
align-items: center;<br />
min-height: 68px;<br />
box-sizing: border-box;<br />
padding: 1rem 1.65rem;<br />
border-top: 1px solid var(--border-color-subtle, #c8ccd1);<br />
color: var(--color-progressive, #36c);<br />
line-height: 1.4;<br />
}<br />
<br />
.terminology-footer-action,<br />
.terminology-footer-action a {<br />
display: inline-flex;<br />
align-items: center;<br />
color: var(--color-progressive, #36c);<br />
text-decoration: none;<br />
}<br />
<br />
.terminology-plus {<br />
display: inline-block;<br />
margin-right: 0.65rem;<br />
font-size: 2rem;<br />
font-weight: 300;<br />
line-height: 0.7;<br />
transform: translateY(-1px);<br />
}<br />
<br />
.terminology-footer-divider {<br />
align-self: stretch;<br />
width: 1px;<br />
max-height: 27px;<br />
margin: 0 1.65rem;<br />
background: var(--border-color-base, #a2a9b1);<br />
}<br />
<br />
@media (max-width: 900px) {<br />
.terminology-header-cell,<br />
.terminology-cell {<br />
padding-right: 1rem;<br />
padding-left: 1rem;<br />
}<br />
<br />
.terminology-row > .terminology-toggle-placeholder,<br />
.terminology-row > .mw-collapsible-toggle {<br />
padding-right: 0.75rem;<br />
padding-left: 0.75rem;<br />
}<br />
}<br />
<br />
@media (max-width: 600px) {<br />
.terminology-footer {<br />
align-items: flex-start;<br />
flex-direction: column;<br />
gap: 0.75rem;<br />
}<br />
<br />
.terminology-footer-divider {<br />
display: none;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Statement/styles.css&diff=217
Template:Statement/styles.css
2026-07-16T10:13:19Z
<p>InfernalAtom683: </p>
<hr />
<div>.global-box.math-statement {<br />
border-left-width: 0.25em;<br />
border-radius: 0;<br />
}<br />
<br />
/* Theorem、Lemma、Proposition 等 */<br />
.global-box.math-statement--proof {<br />
border-left-color: #36c;<br />
}<br />
<br />
/* Definition、Axiom、Notation 等 */<br />
.global-box.math-statement--definition {<br />
border-left-color: #14866d;<br />
}<br />
<br />
/* Conjecture、Hypothesis */<br />
.global-box.math-statement--conjecture {<br />
border-left-color: #7256a8;<br />
}<br />
<br />
/* Example、Counterexample */<br />
.global-box.math-statement--example {<br />
border-left-color: #ac6600;<br />
}<br />
<br />
/* Exercise、Problem、Question */<br />
.global-box.math-statement--task {<br />
border-left-color: #b32424;<br />
}<br />
<br />
/* Remark、Note、Observation 等 */<br />
.global-box.math-statement--expository {<br />
border-left-color: #72777d;<br />
}<br />
<br />
.math-statement .global-box__title {<br />
font-size: 1em;<br />
}<br />
<br />
.math-statement--proof .global-box__details-heading {<br />
font-style: italic;<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Box/styles.css&diff=216
Template:Box/styles.css
2026-07-16T10:13:00Z
<p>InfernalAtom683: </p>
<hr />
<div>.global-box {<br />
box-sizing: border-box;<br />
overflow: hidden;<br />
border: 1px solid #a2a9b1;<br />
border-radius: 0;<br />
margin: 0.65em 1em;<br />
background: #fff;<br />
color: #202122;<br />
}<br />
<br />
.global-box__title {<br />
padding: 0.4em 0.7em 0.05em;<br />
font-weight: 700;<br />
line-height: 1.35;<br />
}<br />
<br />
.global-box__body {<br />
padding: 0.15em 0.7em 0.45em;<br />
line-height: 1.5;<br />
}<br />
<br />
.global-box__details {<br />
border-top: 1px solid #c8ccd1;<br />
padding: 0.35em 0.7em 0.4em;<br />
background: #f8f9fa;<br />
}<br />
<br />
.global-box__details-heading {<br />
min-height: 1.3em;<br />
font-weight: 600;<br />
line-height: 1.3;<br />
}<br />
<br />
.global-box__details .mw-collapsible-toggle {<br />
float: right;<br />
margin-left: 0.75em;<br />
font-size: 0.85em;<br />
font-weight: normal;<br />
}<br />
<br />
.global-box__details-content {<br />
padding-top: 0.3em;<br />
line-height: 1.5;<br />
}<br />
<br />
.global-box__body > :first-child,<br />
.global-box__details-content > :first-child {<br />
margin-top: 0;<br />
}<br />
<br />
.global-box__body > :last-child,<br />
.global-box__details-content > :last-child {<br />
margin-bottom: 0;<br />
}<br />
<br />
@media (max-width: 500px) {<br />
.global-box {<br />
margin: 0.6em 0;<br />
}<br />
<br />
.global-box__title,<br />
.global-box__body,<br />
.global-box__details {<br />
padding-right: 0.55em;<br />
padding-left: 0.55em;<br />
}<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:SubQED/styles.css&diff=215
Template:SubQED/styles.css
2026-07-16T08:40:29Z
<p>InfernalAtom683: </p>
<hr />
<div>.subqed,<br />
.proofqed {<br />
display: inline-block;<br />
float: right;<br />
margin-left: 0.6em;<br />
font-family: serif;<br />
font-style: normal;<br />
font-weight: normal;<br />
line-height: inherit;<br />
white-space: nowrap;<br />
}<br />
<br />
.subqed {<br />
font-size: 1.2em;<br />
}<br />
<br />
.proofqed {<br />
font-size: 1.2em;<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:SubQED/doc&diff=214
Template:SubQED/doc
2026-07-16T08:39:26Z
<p>InfernalAtom683: Created page with "{{Documentation subpage}} The '''SubQED template''' marks the end of a subordinate argument within a proof. It displays a solid square, <math>\blacksquare</math>. The template {{tl|QED}} redirects here. == Usage == Place the template at the end of a claim, case, implication, or other subordinate argument: <pre> Suppose that <math>x\in\ker f</math>. Then <math>f(x)=e</math>, and hence <math>x\in N</math>. {{SubQED}} </pre> It may also be invoked through its shorter..."</p>
<hr />
<div>{{Documentation subpage}}<br />
<br />
The '''SubQED template''' marks the end of a subordinate argument within a proof. It displays a solid square, <math>\blacksquare</math>.<br />
<br />
The template {{tl|QED}} redirects here.<br />
<br />
== Usage ==<br />
<br />
Place the template at the end of a claim, case, implication, or other subordinate argument:<br />
<br />
<pre><br />
Suppose that <math>x\in\ker f</math>. Then <math>f(x)=e</math>, and hence<br />
<math>x\in N</math>. {{SubQED}}<br />
</pre><br />
<br />
It may also be invoked through its shorter alias:<br />
<br />
<pre><br />
{{QED}}<br />
</pre><br />
<br />
== Conventions ==<br />
<br />
The solid square marks the end of a subordinate proof or a distinct stage of an enclosing proof. It should not normally be used after every paragraph or calculation.<br />
<br />
For the end of an entire proof, use {{tl|ProofQED}}, which displays an open square.<br />
<br />
== See also ==<br />
<br />
* {{tl|ProofQED}}<br />
<br />
<includeonly><br />
[[Category:Proof templates]]<br />
</includeonly></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:ProofQED&diff=213
Template:ProofQED
2026-07-16T08:39:03Z
<p>InfernalAtom683: Created page with "<templatestyles src="SubQED/styles.css" /><span class="proofqed" title="End of proof" aria-label="End of proof">□</span><noinclude> {{Documentation}} </noinclude>"</p>
<hr />
<div><templatestyles src="SubQED/styles.css" /><span class="proofqed" title="End of proof" aria-label="End of proof">□</span><noinclude><br />
{{Documentation}}<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:QED&diff=212
Template:QED
2026-07-16T08:38:25Z
<p>InfernalAtom683: Redirected page to Template:SubQED</p>
<hr />
<div>#REDIRECT [[Template:SubQED]]</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:SubQED&diff=211
Template:SubQED
2026-07-16T08:38:04Z
<p>InfernalAtom683: Created page with "<templatestyles src="SubQED/styles.css" /><span class="subqed" title="End of subproof" aria-label="End of subproof">■</span><noinclude> {{Documentation}} </noinclude>"</p>
<hr />
<div><templatestyles src="SubQED/styles.css" /><span class="subqed" title="End of subproof" aria-label="End of subproof">■</span><noinclude><br />
{{Documentation}}<br />
</noinclude></div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:SubQED/styles.css&diff=210
Template:SubQED/styles.css
2026-07-16T08:37:55Z
<p>InfernalAtom683: Created page with ".subqed, .proofqed { display: inline-block; float: right; margin-left: 0.6em; font-family: serif; font-style: normal; font-weight: normal; line-height: inherit; white-space: nowrap; } .subqed { font-size: 0.85em; } .proofqed { font-size: 1em; }"</p>
<hr />
<div>.subqed,<br />
.proofqed {<br />
display: inline-block;<br />
float: right;<br />
margin-left: 0.6em;<br />
font-family: serif;<br />
font-style: normal;<br />
font-weight: normal;<br />
line-height: inherit;<br />
white-space: nowrap;<br />
}<br />
<br />
.subqed {<br />
font-size: 0.85em;<br />
}<br />
<br />
.proofqed {<br />
font-size: 1em;<br />
}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Counterexample&diff=209
Template:Counterexample
2026-07-16T08:36:29Z
<p>InfernalAtom683: Created page with "{{Statement | type=counterexample | title={{{title|Counterexample}}} | content={{{counterexample|{{{1|}}}}}} | details={{{explanation|{{{2|}}}}}} | details-title={{{explanation-title|Explanation}}} | open={{{explanation-open|no}}} | expand-text={{{explanation-expand-text|}}} | collapse-text={{{explanation-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=counterexample<br />
| title={{{title|Counterexample}}}<br />
| content={{{counterexample|{{{1|}}}}}}<br />
| details={{{explanation|{{{2|}}}}}}<br />
| details-title={{{explanation-title|Explanation}}}<br />
| open={{{explanation-open|no}}}<br />
| expand-text={{{explanation-expand-text|}}}<br />
| collapse-text={{{explanation-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Example&diff=208
Template:Example
2026-07-16T08:36:14Z
<p>InfernalAtom683: Created page with "{{Statement | type=example | title={{{title|Example}}} | content={{{example|{{{1|}}}}}} | details={{{explanation|{{{2|}}}}}} | details-title={{{explanation-title|Explanation}}} | open={{{explanation-open|no}}} | expand-text={{{explanation-expand-text|}}} | collapse-text={{{explanation-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=example<br />
| title={{{title|Example}}}<br />
| content={{{example|{{{1|}}}}}}<br />
| details={{{explanation|{{{2|}}}}}}<br />
| details-title={{{explanation-title|Explanation}}}<br />
| open={{{explanation-open|no}}}<br />
| expand-text={{{explanation-expand-text|}}}<br />
| collapse-text={{{explanation-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Warning&diff=207
Template:Warning
2026-07-16T08:35:52Z
<p>InfernalAtom683: Created page with "{{Statement | type=warning | title={{{title|Warning}}} | content={{{warning|{{{1|}}}}}} | details={{{details|{{{2|}}}}}} | details-title={{{details-title|Details}}} | open={{{details-open|no}}} | expand-text={{{details-expand-text|}}} | collapse-text={{{details-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=warning<br />
| title={{{title|Warning}}}<br />
| content={{{warning|{{{1|}}}}}}<br />
| details={{{details|{{{2|}}}}}}<br />
| details-title={{{details-title|Details}}}<br />
| open={{{details-open|no}}}<br />
| expand-text={{{details-expand-text|}}}<br />
| collapse-text={{{details-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Observation&diff=206
Template:Observation
2026-07-16T08:35:41Z
<p>InfernalAtom683: Created page with "{{Statement | type=observation | title={{{title|Observation}}} | content={{{observation|{{{1|}}}}}} | details={{{details|{{{2|}}}}}} | details-title={{{details-title|Details}}} | open={{{details-open|no}}} | expand-text={{{details-expand-text|}}} | collapse-text={{{details-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=observation<br />
| title={{{title|Observation}}}<br />
| content={{{observation|{{{1|}}}}}}<br />
| details={{{details|{{{2|}}}}}}<br />
| details-title={{{details-title|Details}}}<br />
| open={{{details-open|no}}}<br />
| expand-text={{{details-expand-text|}}}<br />
| collapse-text={{{details-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Note&diff=205
Template:Note
2026-07-16T08:35:27Z
<p>InfernalAtom683: Created page with "{{Statement | type=note | title={{{title|Note}}} | content={{{note|{{{1|}}}}}} | details={{{details|{{{2|}}}}}} | details-title={{{details-title|Details}}} | open={{{details-open|no}}} | expand-text={{{details-expand-text|}}} | collapse-text={{{details-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=note<br />
| title={{{title|Note}}}<br />
| content={{{note|{{{1|}}}}}}<br />
| details={{{details|{{{2|}}}}}}<br />
| details-title={{{details-title|Details}}}<br />
| open={{{details-open|no}}}<br />
| expand-text={{{details-expand-text|}}}<br />
| collapse-text={{{details-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Remark&diff=204
Template:Remark
2026-07-16T08:35:15Z
<p>InfernalAtom683: Created page with "{{Statement | type=remark | title={{{title|Remark}}} | content={{{remark|{{{1|}}}}}} | details={{{details|{{{2|}}}}}} | details-title={{{details-title|Details}}} | open={{{details-open|no}}} | expand-text={{{details-expand-text|}}} | collapse-text={{{details-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=remark<br />
| title={{{title|Remark}}}<br />
| content={{{remark|{{{1|}}}}}}<br />
| details={{{details|{{{2|}}}}}}<br />
| details-title={{{details-title|Details}}}<br />
| open={{{details-open|no}}}<br />
| expand-text={{{details-expand-text|}}}<br />
| collapse-text={{{details-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Criterion&diff=203
Template:Criterion
2026-07-16T08:35:05Z
<p>InfernalAtom683: Created page with "{{Statement | type=criterion | title={{{title|Criterion}}} | content={{{criterion|{{{1|}}}}}} | details={{{proof|{{{2|}}}}}} | details-title={{{proof-title|Proof}}} | open={{{proof-open|no}}} | expand-text={{{proof-expand-text|}}} | collapse-text={{{proof-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=criterion<br />
| title={{{title|Criterion}}}<br />
| content={{{criterion|{{{1|}}}}}}<br />
| details={{{proof|{{{2|}}}}}}<br />
| details-title={{{proof-title|Proof}}}<br />
| open={{{proof-open|no}}}<br />
| expand-text={{{proof-expand-text|}}}<br />
| collapse-text={{{proof-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Identity&diff=202
Template:Identity
2026-07-16T08:34:52Z
<p>InfernalAtom683: Created page with "{{Statement | type=identity | title={{{title|Identity}}} | content={{{identity|{{{1|}}}}}} | details={{{proof|{{{2|}}}}}} | details-title={{{proof-title|Proof}}} | open={{{proof-open|no}}} | expand-text={{{proof-expand-text|}}} | collapse-text={{{proof-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=identity<br />
| title={{{title|Identity}}}<br />
| content={{{identity|{{{1|}}}}}}<br />
| details={{{proof|{{{2|}}}}}}<br />
| details-title={{{proof-title|Proof}}}<br />
| open={{{proof-open|no}}}<br />
| expand-text={{{proof-expand-text|}}}<br />
| collapse-text={{{proof-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Property&diff=201
Template:Property
2026-07-16T08:34:21Z
<p>InfernalAtom683: </p>
<hr />
<div>{{Statement<br />
| type=property<br />
| title={{{title|Property}}}<br />
| content={{{property|{{{1|}}}}}}<br />
| details={{{proof|{{{2|}}}}}}<br />
| details-title={{{proof-title|Proof}}}<br />
| open={{{proof-open|no}}}<br />
| expand-text={{{proof-expand-text|}}}<br />
| collapse-text={{{proof-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Result&diff=200
Template:Result
2026-07-16T08:34:08Z
<p>InfernalAtom683: Created page with "{{Statement | type=result | title={{{title|Result}}} | content={{{result|{{{1|}}}}}} | details={{{proof|{{{2|}}}}}} | details-title={{{proof-title|Proof}}} | open={{{proof-open|no}}} | expand-text={{{proof-expand-text|}}} | collapse-text={{{proof-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=result<br />
| title={{{title|Result}}}<br />
| content={{{result|{{{1|}}}}}}<br />
| details={{{proof|{{{2|}}}}}}<br />
| details-title={{{proof-title|Proof}}}<br />
| open={{{proof-open|no}}}<br />
| expand-text={{{proof-expand-text|}}}<br />
| collapse-text={{{proof-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683
https://www.mathepedia.wiki/w/index.php?title=Template:Fact&diff=199
Template:Fact
2026-07-16T08:33:51Z
<p>InfernalAtom683: Created page with "{{Statement | type=fact | title={{{title|Fact}}} | content={{{fact|{{{1|}}}}}} | details={{{proof|{{{2|}}}}}} | details-title={{{proof-title|Proof}}} | open={{{proof-open|no}}} | expand-text={{{proof-expand-text|}}} | collapse-text={{{proof-collapse-text|}}} | style={{{style|}}} | class={{{class|}}} }}"</p>
<hr />
<div>{{Statement<br />
| type=fact<br />
| title={{{title|Fact}}}<br />
| content={{{fact|{{{1|}}}}}}<br />
| details={{{proof|{{{2|}}}}}}<br />
| details-title={{{proof-title|Proof}}}<br />
| open={{{proof-open|no}}}<br />
| expand-text={{{proof-expand-text|}}}<br />
| collapse-text={{{proof-collapse-text|}}}<br />
| style={{{style|}}}<br />
| class={{{class|}}}<br />
}}</div>
InfernalAtom683