Solution
= Solution
For each $N$, only finitely many <permutation>[permutations] fix every $j>N$: they are precisely the permutations of $\{1,\ldots,N\}$. Thus
$$
C=\bigcup_{N\geq1}S_N
$$
is a countable union of finite sets and is countable.
= Solution
For each $N$, only finitely many <permutation>[permutations] fix every $j>N$: they are precisely the permutations of $\{1,\ldots,N\}$. Thus
$$
C=\bigcup_{N\geq1}S_N
$$
is a countable union of finite sets and is countable.