continuity – Is $f$ continuous at $0$?

$f : [0, 1] → mathbb{R}$

$f(x) := inf{|nx − 1| : n ∈ mathbb{N}}$

I found that $f(x)$ is continuous on $big(dfrac{1}{m+1}, dfrac1mbig]$
and that $displaystyle lim_{xto 0}f(x)=0$

How can I say if $f(x)$ is continuous at $0$ with these facts?