# Give an example of a function $f\colon\mathbb{R}\to\mathbb{R}$ which is continuous except at the integers

I need an example please. I am not sure how to provide an example

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$f(x) = \lfloor x \rfloor$ – Will Jagy Oct 15 '12 at 20:44
$f(x) = \chi_{\mathbb{R}-\mathbb{Z}}$ – Neal Oct 15 '12 at 20:44
As you may have realized from the various suggested examples, the idea is to start with a picture of a nice continuous function in your head and then make it jump at every integer. – Atul Ingle Oct 15 '12 at 21:05

An indicator function for integers $I_\mathbb{Z}(x)$:
$f(x)=1$ when $x \in \mathbb{Z}$ i.e. $x$ is an integer
$f(x)=0$ when $x \not\in \mathbb{Z}$ i.e. $x$ is not an integer