Let $X \subseteq \mathbb{R}$ be a subset. Let $\{f_n\}$ be a sequence of real valued functions such that $f_n \to f$ uniformly on $X$. Let $D_n$ denote the set of discontinuities of each $f_n$ and $D$ denotes the set of discontinuities of $f$. Then, can we say that $|D| \leq |D_n|$?
The result seems to be true but unable to prove it.