Definition 1.13

Definition 1.13: If $$x_1, x_2, \dots \in X$$ is a sequence of points in $$X$$ and $$x \in X$$ is a point, we say that the sequence $$x_n$$ converges to $$x$$, written $$\lim_{n \rightarrow \infty} x_n = x$$ or $$x_n \rightarrow x$$ if for every $$\epsilon > 0$$ there is some $$N$$ large enough that for every $$n \geq N$$, $$x_n \in B(x, \epsilon)$$