Difference between revisions of "Dirichlet function"
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(Created page with "The Dirichlet function $D \colon \mathbb{R} \rightarrow \{0,1\}$ is defined by $$D(x) = \left\{ \begin{array}{ll} 1, & y \in \mathbb{Q} \\ 0, & y \in \mathbb{R} \setminus \mat...") |
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=Properties= | =Properties= | ||
| + | [[Dirichlet function is nowhere continuous]]<br /> | ||
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| + | =See also= | ||
| + | [[Thomae function]]<br /> | ||
=References= | =References= | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 07:29, 10 January 2017
The Dirichlet function $D \colon \mathbb{R} \rightarrow \{0,1\}$ is defined by $$D(x) = \left\{ \begin{array}{ll} 1, & y \in \mathbb{Q} \\ 0, & y \in \mathbb{R} \setminus \mathbb{Q}, \end{array} \right.$$ where $\mathbb{Q}$ denotes the set of rational numbers and $\mathbb{R} \setminus \mathbb{Q}$ denotes the set of irrational number.
Properties
Dirichlet function is nowhere continuous
