# Definition:Thomae Function

## Definition

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)

## Also known as

The Thomae function is also seen styled as Thomae's Function.

It has several names in the literature:

## Also see

• Results about the Thomae function can be found here.

## Source of Name

This entry was named for Carl Johannes Thomae.