# 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?