@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-FF99PJ0L-W
  skos:prefLabel "algebraic function"@en, "fonction algébrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-WWSM7CVR-6 .

psr:-WWSM7CVR-6
  skos:altLabel "identity transformation"@en, "application identité"@fr, "identity relation"@en, "identity map"@en ;
  skos:definition """In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when <i>f</i> is the identity function, the equality <i>f</i>(<i>X</i>) = <i>X</i> is true for all values of <i>X</i> to which <i>f</i> can be applied. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Identity_function">https://en.wikipedia.org/wiki/Identity_function</a>)"""@en, """En mathématiques,  l'<b>application identité</b> ou la <b>fonction identité</b> est l'application qui n'a aucun effet lorsqu'elle est appliquée à un élément&nbsp;: elle renvoie l'argument sur lui-même. Formellement, sur un ensemble <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>E</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span>, c'est l'application&nbsp;:
<br/>
<br/><center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\egin{array}{l|rcl}\\\\mathrm {id} _{E}:&amp;E&amp;\\\\longrightarrow &amp;E\\\\\\\\&amp;x&amp;\\\\longmapsto &amp;x\\\\end{array}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtable columnalign="left right center left" rowspacing="4pt" columnspacing="1em" columnlines="solid none none">
<br/>            <mtr>
<br/>              <mtd>
<br/>                <msub>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi mathvariant="normal">i</mi>
<br/>                    <mi mathvariant="normal">d</mi>
<br/>                  </mrow>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>E</mi>
<br/>                  </mrow>
<br/>                </msub>
<br/>                <mo>:</mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi>E</mi>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">⟶<!-- ⟶ --></mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi>E</mi>
<br/>              </mtd>
<br/>            </mtr>
<br/>            <mtr>
<br/>              <mtd></mtd>
<br/>              <mtd>
<br/>                <mi>x</mi>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mo stretchy="false">⟼<!-- ⟼ --></mo>
<br/>              </mtd>
<br/>              <mtd>
<br/>                <mi>x</mi>
<br/>              </mtd>
<br/>            </mtr>
<br/>          </mtable>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{array}{l|rcl}\\\\mathrm {id} _{E}:&amp;E&amp;\\\\longrightarrow &amp;E\\\\\\\\&amp;x&amp;\\\\longmapsto &amp;x\\\\end{array}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b0c5ef862856dfdd4f7d8bf7c064a1f9d488500" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:21.653ex; height:7.176ex;" alt="{\\\\displaystyle {\\egin{array}{l|rcl}\\\\mathrm {id} _{E}:&amp;E&amp;\\\\longrightarrow &amp;E\\\\\\\\&amp;x&amp;\\\\longmapsto &amp;x\\\\end{array}}}"></span></center>
<br/>Le graphe de l'application identité de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>E</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span> est appelé la diagonale du produit cartésien <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E\\	imes E}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>E</mi>
<br/>        <mo>×<!-- × --></mo>
<br/>        <mi>E</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle E\\	imes E}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/438347ffb26c796eaac13d2e0cceb8a6a1ad1598" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.392ex; height:2.176ex;" alt="{\\\\displaystyle E\\	imes E}"></span>. Pour <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E=\\\\mathbb {R} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>E</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle E=\\\\mathbb {R} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/403069620dea86b725997dd3b085172bd11f1bec" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.552ex; height:2.176ex;" alt="{\\\\displaystyle E=\\\\mathbb {R} }"></span> l'ensemble des réels, ce graphe est la première bissectrice du plan euclidien. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Application_identit%C3%A9">https://fr.wikipedia.org/wiki/Application_identit%C3%A9</a>)"""@fr ;
  skos:prefLabel "identity function"@en, "fonction identité"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Application_identit%C3%A9>, <https://en.wikipedia.org/wiki/Identity_function> ;
  skos:broader psr:-FF99PJ0L-W, psr:-T88XBMNP-M ;
  dc:modified "2023-08-21"^^xsd:date ;
  skos:inScheme psr: ;
  a skos:Concept .

psr:-T88XBMNP-M
  skos:prefLabel "set theory"@en, "théorie des ensembles"@fr ;
  a skos:Concept ;
  skos:narrower psr:-WWSM7CVR-6 .