[45] A sequence (a_m) of points in R^n converges to b = (b_1, b_2,..., b_n) ⇔ 1≦∀k≦n, (a_{m,k})m∈N converges to b_k.

https://www.evernote.com/shard/s29/sh/6b698804-7ddf-4cee-909d-64234c384caa/0af43d636e71745c6edb25d992fb26db