Supply a proof for the following theorem: Suppose that f is continuous at a and that x(subscript)n tends to a as n goes to infinity. Then there is an integer N such that f(x(subscript)n) is defined for all integers n > N; furthermore, f(x(subscript)n) tends to f(a) as n goes to infinity.
Should I be typing these in LaTeX and posting them here somehow? I hope it is obvious that typing this out with regular script that x(subscript)n represents the sequence x-sub-n. This is my first post so I hope to clean up my future posts before submission to aviod confusion or ambiguity.