## Calculus (3rd Edition)

$f(x)=[x]$ has a jump discontinuity at $x=n$.
The function $f(x)=[x]$, has a jump discontinuity at $x=n$ for every integer $n$, since $$\lim _{x \rightarrow n+}[x]=n, \quad \lim _{x \rightarrow n-}[x]=n-1.$$ Moreover, $f(x)=[x]$ is right-continuous, but not left continuous.