Question: Prove at x=0 that cos(1/x) does not have a removable discontinuity.

Attempt: I used two sequences that as limit n-> infinity, each sequence goes to zero, but if I insert the sequences into cos(1/x), cos(1/{xn}) goes to -1 and cos(1/{yn}) goes to 1. Does this show that at x=0, cos(1/x) does not have a removable discontinuity?