$f : [0, 1] → mathbb{R}$

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

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

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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?

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