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**paulread** 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.