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

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    $f(x) = \lfloor x \rfloor$2012-10-15
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    $f(x) = \chi_{\mathbb{R}-\mathbb{Z}}$2012-10-15
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    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.2012-10-15

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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