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But the given theorem only states that, "if a sequence of functions is continuous and converges uniformly to f, then f is continuous."

I'm given that f is not continuous. and that the fourieer series of f is not continuous. How does this mean that the fourieer series doesnt converge uniformly to f?

This is just a application of logic here

A&B=> C

not C=> (not A) or (not B)

knowing (not A) doesnt really give me (not B)