Suppose $f:\frac{1}{6}\mathbb{Z}\to\frac{1}{6}\mathbb{Z}$ is a function defined by $f(n):=n,6n\in\mathbb{Z}$. Is $f$ continuous at $x=0$? A graph of the function somewhat points towards this answer:
Although I may be wrong, to me it appears that $\lim\limits_{x\to0}f(x)=0=f(0)$. However, I am wondering how one may go about constructing $\varepsilon-\delta$ proof if this is indeed the case.
Thank you.