How can I show that this function is discontinuous at the point $x=1$?

Suppose you had the function
$$
f(x) = ; text{ the integer part of } x
$$
I wish to show that this is not continuous at the point $x=1$, which I will try to do by showing that $lim_{x rightarrow 1} f(x)$ does not exist. To do this, I use a direct $varepsilon – delta$ proof of convergence. That is, show that for some arbitrary value of $varepsilon$ there exists no value of $delta$ such that
$$
0 < |x-1| < delta Rightarrow |f(x) – L| < varepsilon
$$
I am not sure where to go from here. Can anyone please help.