I need an example please. I am not sure how to provide an example
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asked Oct 15, 2012 at 20:42
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10$\begingroup$ $f(x) = \lfloor x \rfloor$ $\endgroup$– Will JagyCommented Oct 15, 2012 at 20:44
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5$\begingroup$ $f(x) = \chi_{\mathbb{R}-\mathbb{Z}}$ $\endgroup$– NealCommented Oct 15, 2012 at 20:44
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2$\begingroup$ 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. $\endgroup$– Atul IngleCommented Oct 15, 2012 at 21:05
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1 Answer
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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
