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## Main Question or Discussion Point

Can anyone explain to me why if a sequence of functions {f_n} is uniformly convergent, then it must converge to it's pointwise limit?

So, if we showed {f_n} is

So, if we showed {f_n} is

*not*uniformly convergent to some f (f is the pointwise limit), how do we know that there isn't some other function, say g, such that {f_n} converges to g uniformly?