Need to know how to prove that a sequence $\{x_k\}_{k=1}^\infty\subset \mathbb{R}^n$ converges to $x$ if and only if the map $ f:\{1,2,3...\} \to\mathbb{R}^n$, $ f(j) = x_j$, is continuous.
It's been puzzling me for the last few hours now. I know that a sequence converges to a point just when every open set containing x contains all but finitely many of the points in the sequence.