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In mathematics, the Dirichlet function is the indicator function 1Q or 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q, i.e. 1Q = 1 if x is a rational number and 1Q = 0 if x is not a rational number.
It is named after the mathematician Peter Gustav Lejeune Dirichlet. It is an example of pathological function which provides counterexamples to many situations.
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