@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:-GJ7QW40K-0
  a skos:Concept ;
  skos:broader psr:-FH1H1FB9-1, psr:-MDFZ99KQ-Q, psr:-DMTN3C45-S ;
  skos:prefLabel "Dirichlet function"@en, "fonction de Dirichlet"@fr ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Dirichlet_function>, <https://fr.wikipedia.org/wiki/Fonction_de_Dirichlet> ;
  skos:definition """En mathématiques, la <b>fonction de Dirichlet</b> est la fonction indicatrice <b>1</b><sub>ℚ</sub> de l'ensemble des rationnels ℚ, c'est-à-dire que <b>1</b><sub>ℚ</sub>(<i>x</i>) = 1 si <i>x</i> est un nombre rationnel et <b>1</b><sub>ℚ</sub>(<i>x</i>) = 0 si <i>x</i> n'est un pas un nombre rationnel (c'est-à-dire un nombre irrationnel).
<br/>Elle est nommée en l'honneur du mathématicien Peter Gustav Lejeune Dirichlet. C'est un exemple de fonction pathologique qui fournit un contre-exemple à beaucoup de situations. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_de_Dirichlet">https://fr.wikipedia.org/wiki/Fonction_de_Dirichlet</a>)"""@fr, """In mathematics, the <b>Dirichlet function</b> is the indicator function <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 \\\\mathbf {1} _{\\\\mathbb {Q} }}">
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<br/>            <mn mathvariant="bold">1</mn>
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<br/>              <mi mathvariant="double-struck">Q</mi>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }}</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e49bd45fd57b71a4050878506a5f2e6719fbfef" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:2.847ex; height:2.676ex;" alt="{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }}"></span> of the set of rational numbers <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 \\\\mathbb {Q} }">
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<mi mathvariant="double-struck">Q</mi>
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<annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Q} }</annotation>
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="\\\\mathbb {Q} "></span>, i.e. <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 \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
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<mn mathvariant="bold">1</mn>
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<mi mathvariant="double-struck">Q</mi>
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<annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=1}</annotation>
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3638e1da26e9032c99ca7118783e4bbb91b7bf14" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.247ex; height:2.843ex;" alt="{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=1}"></span> if <span class="texhtml mvar" style="font-style:italic;">x</span> is a rational number and <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 \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=0}">
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<annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=0}</annotation>
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52fa2d4269db667a8e6b07344666f4cfbf1c7ff0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.247ex; height:2.843ex;" alt="{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)=0}"></span> if <span class="texhtml mvar" style="font-style:italic;">x</span> is not a rational number (i.e. is an irrational number).
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)={\\egin{cases}1&amp;x\\\\in \\\\mathbb {Q} \\\\\\\\0&amp;x\\
otin \\\\mathbb {Q} \\\\end{cases}}}">
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)={\\egin{cases}1&amp;x\\\\in \\\\mathbb {Q} \\\\\\\\0&amp;x\\
otin \\\\mathbb {Q} \\\\end{cases}}}</annotation>
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<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9644752f79f150fc7f884e3f8b8f4dcaa9109706" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.505ex; width:21.043ex; height:6.176ex;" alt="{\\\\displaystyle \\\\mathbf {1} _{\\\\mathbb {Q} }(x)={\\egin{cases}1&amp;x\\\\in \\\\mathbb {Q} \\\\\\\\0&amp;x\\
otin \\\\mathbb {Q} \\\\end{cases}}}"></div>
<br/>It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of pathological function which provides counterexamples to many situations. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_function">https://en.wikipedia.org/wiki/Dirichlet_function</a>)"""@en ;
  dc:created "2023-07-26"^^xsd:date ;
  dc:modified "2023-07-26"^^xsd:date .

psr: a skos:ConceptScheme .
psr:-MDFZ99KQ-Q
  skos:prefLabel "fonction numérique"@fr, "real-valued function"@en ;
  a skos:Concept ;
  skos:narrower psr:-GJ7QW40K-0 .

psr:-FH1H1FB9-1
  skos:prefLabel "special function"@en, "fonction spéciale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-GJ7QW40K-0 .

psr:-DMTN3C45-S
  skos:prefLabel "fonction caractéristique"@fr, "characteristic function"@en ;
  a skos:Concept ;
  skos:narrower psr:-GJ7QW40K-0 .