: Mathematics: Dirichlet function

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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)

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