# Math Help - Sequence of functions

1. ## Sequence of functions

Let (fn) be a sequence of functions from R to R, not necessarily continuous. Suppose that for all sequences (xn) such that (xn)-->x as n--> inf, we have:

(fn(xn)) --> f(x) as n-->inf and (xn)-->x

Prove that f is continuous.

PS: No specific metric is identified

2. Originally Posted by southprkfan1
Let (fn) be a sequence of functions from R to R, not necessarily continuous. Suppose that for all sequences (xn) such that (xn)-->x as n--> inf, we have:

(fn(xn)) --> f(x) as n-->inf and (xn)-->x

Prove that f is continuous.

PS: No specific metric is identified