Category:Thomae Function

This category contains results about the Thomae function.

Thomae Function on $\openint 0 1$

The Thomae function $D_M: \R \to \R$ is the real function defined as:

$\forall x \in \R: \map {D_M} x = \begin {cases} 0 & : x = 0 \text { or } x \notin \Q \\ \dfrac 1 q & : x = \dfrac p q : p \perp q, q > 0 \end {cases}$

where:

$\Q$ denotes the set of rational numbers

$p \perp q$ denotes that $p$ and $q$ are coprime (that is, $x$ is a rational number expressed in canonical form)