$f : [0, 1] → mathbb{R}$
$f(x) := inf{|nx − 1| : n ∈ mathbb{N}}$
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?
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$f : [0, 1] → mathbb{R}$
$f(x) := inf{|nx − 1| : n ∈ mathbb{N}}$
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?