@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:-ZTD7VMDS-3
  skos:prefLabel "analyse convexe"@fr, "convex analysis"@en ;
  a skos:Concept ;
  skos:related psr:-CK2Z2K3F-G .

psr:-W42D202L-K
  skos:prefLabel "inégalité"@fr, "inequality"@en ;
  a skos:Concept ;
  skos:narrower psr:-CK2Z2K3F-G .

psr:-CK2Z2K3F-G
  skos:prefLabel "Bernoulli's inequality"@en, "inégalité de Bernoulli"@fr ;
  dc:created "2023-08-11"^^xsd:date ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1+x. It is often employed in real analysis. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Bernoulli%27s_inequality">https://en.wikipedia.org/wiki/Bernoulli%27s_inequality</a>)"""@en, """En analyse, l'<b>inégalité de Bernoulli</b> — portant le nom du mathématicien Jacques Bernoulli — énonce que :  <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 (1+x)^{n}>1+nx}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo stretchy="false">(</mo>         <mn>1</mn>         <mo>+</mo>         <mi>x</mi>         <msup>           <mo stretchy="false">)</mo>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msup>         <mo>&gt;</mo>         <mn>1</mn>         <mo>+</mo>         <mi>n</mi>         <mi>x</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle (1+x)^{n}&gt;1+nx}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7f4873cff512dd3dfe840e3574d74a4c282cd3d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.186ex; height:2.843ex;" alt="{\\\\displaystyle (1+x)^{n}>1+nx}"></span></center> pour tout entier </span> <span class="texhtml"><i>n</i> &gt; 1</span> et tout réel <span class="texhtml mvar" style="font-style:italic;">x</span> non nul supérieur ou égal à <span class="texhtml">−1</span>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_de_Bernoulli">https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_de_Bernoulli</a>)"""@fr ;
  skos:broader psr:-W42D202L-K ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Bernoulli%27s_inequality>, <https://fr.wikipedia.org/wiki/In%C3%A9galit%C3%A9_de_Bernoulli> ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:related psr:-ZTD7VMDS-3 .