Let $f:\Bbb N \to\Bbb R$ by writing $f(n) = \frac1{n^2}$. Is $f$ continuous at any point in its domain.
So, my thought is, $f$ is a function with domain $\Bbb N$ - natural numbers, so each point in the domain of $f$ is isolated.
So, according to the Limit Version of continuity, the function $f$ is contiuous at $x_0$ provided that $x_0$ is isolated in $A$, or else, $x$ is a point of accumulation (and $\Bbb N$ has none) so
$\lim_{x\to x_0}f(x) = f(x_0)\;.$
So $f$ is continuous at any point in its domain.
I'm really not too sure about my answer (or the way I answered it). So please let me know what you think. Thanks