Suppose X_{n} $X_n$ are finite sets for any natural integer n. $n$. let Y $Y$ be an infinite subset of TT X_{n}$\prod_n X_n$. Does Do there exist y $y$ and y' $y'$ in Y $Y$ and an infinite subset S $S$ of \mathad{N} $\mathbb N$ such that y_{n}=y'_{n} $y_n=y'_n$ for all n $n$ in S ?$S$?

Suppose X_{n} are finite sets for any natural integer n. let Y be an infinite subset of TT X_{n}. Does there exist y and y' in Y and infinite subset S of \mathad{N} such that y_{n}=y'_{n} for all n in S ?