: Mathématiques: Dirichlet function

mathematical physics > special function > Dirichlet function

mathematical analysis > functional analysis > special function > Dirichlet function

mathematical analysis > real analysis > real-valued function > Dirichlet function

set theory > characteristic function > Dirichlet function

mathematical analysis > function > characteristic function > Dirichlet function

Dirichlet function

In mathematics, the Dirichlet function is the indicator function ${\\displaystyle \\mathbf {1} _{\\mathbb {Q} }}$ of the set of rational numbers ${\\displaystyle \\mathbb {Q} }$ , i.e. ${\\displaystyle \\mathbf {1} _{\\mathbb {Q} }(x)=1}$ if $x$ is a rational number and ${\\displaystyle \\mathbf {1} _{\\mathbb {Q} }(x)=0}$ if $x$ is not a rational number (i.e. is an irrational number).
${\\displaystyle \\mathbf {1} _{\\mathbb {Q} }(x)={\egin{cases}1&x\\in \\mathbb {Q} \\\\0&x\ otin \\mathbb {Q} \\end{cases}}}$
It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of pathological function which provides counterexamples to many situations.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Dirichlet_function)

http://data.loterre.fr/ark:/67375/PSR-GJ7QW40K-0

RDF/XML TURTLE JSON-LD Date de création 26/07/2023, dernière modification le 26/07/2023

Loterre