I came upon this statement in stack exchange. Can't remember where.
Statement : If $f_n$ is a sequence of functions (not necessarily continuous) on $[0,1]$ such that $f_n$ converges point-wise to $0$, then there exists an infinite subset of $[0,1]$ where the convergence is uniform.
I couldn't prove it. I believe the claim is true because $[0,1]$ is uncountable but the set of sequences is countable only.
Any help would be appreciated in assistance to how to prove it.