Function that is defined over the entire real number line but continuous nowhere.

[meistertom]

I'm looking for the function that is defined over the entire real number line but continuous nowhere. As well as the person who discovered this. I've been looking this one up for a while but I'm not exactly sure if I'm getting the right one.

 

[pka]

As well as the person who discovered this. I've been looking this one up for a while but I'm not exactly sure if I'm getting the right one.

\(\displaystyle D(x) = \left\{ {\begin{array}{lr}
{1,}&{x \in \mathbb{Q}}\\
{0,}&\text{else}
\end{array}} \right.\)
\(\displaystyle \mathbb{Q}\) stands for the set of rational numbers.

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