[Sequence of functions] A not so nice sequence of function

Let x be irrational, then fn(x)=0 for all n. If x is rational, there exist N natural so that rN=x. For all n>N, fn(x)=0. There you have your point convergence
Let fn converge to f point wise. fn converges uniformly if and only if sup|fn-f| tends to 0. Since there are an infinite number of rationals in any interval, this is evidently not the case.

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