@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:-Z1B19BG4-0
  skos:prefLabel "approximation diophantienne"@fr, "Diophantine approximation"@en ;
  a skos:Concept ;
  skos:related psr:-NWMQVMJQ-1 .

psr: a skos:ConceptScheme .
psr:-NWMQVMJQ-1
  skos:related psr:-Z1B19BG4-0 ;
  skos:inScheme psr: ;
  skos:definition """In mathematics, a <b>rational number</b> is a number that can be expressed as the quotient or fraction <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 {\\	frac {p}{q}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="false" scriptlevel="0">
         <mfrac>
         <mi>p</mi>
         <mi>q</mi>
         </mfrac>
         </mstyle>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {\\	frac {p}{q}}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b38d2684323653daafdd152b7e988594003897d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.663ex; height:3.676ex;" alt="{\\\\displaystyle {\\	frac {p}{q}}}"></span> of two integers, a numerator <span class="texhtml mvar" style="font-style:italic;">p</span> and a non-zero denominator <span class="texhtml mvar" style="font-style:italic;">q</span>. For example, <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 {\\	frac {3}{7}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="false" scriptlevel="0">
         <mfrac>
         <mn>3</mn>
         <mn>7</mn>
         </mfrac>
         </mstyle>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {\\	frac {3}{7}}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15f2b824decf224d9a3143d4271666c7fba7ac83" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\\\\displaystyle {\\	frac {3}{7}}}"></span> is a rational number, as is every integer (e.g., <span class="nowrap"><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 -5={\\	frac {-5}{1}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo>−<!-- − --></mo>
         <mn>5</mn>
         <mo>=</mo>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="false" scriptlevel="0">
         <mfrac>
         <mrow>
         <mo>−<!-- − --></mo>
         <mn>5</mn>
         </mrow>
         <mn>1</mn>
         </mfrac>
         </mstyle>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle -5={\\	frac {-5}{1}}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bef5aab2ced61ba1099051521167fbbe0d346e75" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.006ex; height:3.676ex;" alt="{\\\\displaystyle -5={\\	frac {-5}{1}}}"></span>).</span> The set of all rational numbers, also referred to as "<b>the rationals</b>", the <b>field of rationals</b> or the <b>field of rational numbers</b> is usually denoted by boldface <span class="texhtml"><b>Q</b></span>, or blackboard bold <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} .}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">Q</mi>
         </mrow>
         <mo>.</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Q} .}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/869719f08f506bf866043442858fb3da1d4b4b5b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.455ex; height:2.509ex;" alt="{\\\\displaystyle \\\\mathbb {Q} .}">
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Rational_number">https://en.wikipedia.org/wiki/Rational_number</a>)"""@en, """Un nombre rationnel est, en mathématiques, un nombre qui peut s'exprimer comme le quotient de deux entiers relatifs. On peut ainsi écrire les nombres rationnels sous forme de fractions notées de la façon suivante :
         <dl><dd><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 {\\rac {a}{b}}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mfrac>
         <mi>a</mi>
         <mi>b</mi>
         </mfrac>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {a}{b}}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fbb66e57f89debc3cde3213de12228971148a93" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:2.066ex; height:4.843ex;" alt="{\\rac {a}{b}}"></span></dd></dl>
         <br/>où <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 a}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>a</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle a}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="a"></span>, le numérateur, est un entier relatif et <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 b}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>b</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle b}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="b"></span>, le dénominateur, est un entier relatif non nul.
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_rationnel">https://fr.wikipedia.org/wiki/Nombre_rationnel</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_rationnel>, <https://en.wikipedia.org/wiki/Rational_number> ;
  skos:broader psr:-Z5NBGSJC-F ;
  a skos:Concept ;
  skos:narrower psr:-DVT9K125-N ;
  skos:prefLabel "nombre rationnel"@fr, "rational number"@en ;
  dc:modified "2023-08-24"^^xsd:date .

psr:-Z5NBGSJC-F
  skos:prefLabel "nombre"@fr, "number"@en ;
  a skos:Concept ;
  skos:narrower psr:-NWMQVMJQ-1 .

psr:-DVT9K125-N
  skos:prefLabel "dyadic rational"@en, "rationnel dyadique"@fr ;
  a skos:Concept ;
  skos:broader psr:-NWMQVMJQ-1 .