= Solution
Write $A=\{a_1,\ldots,a_m\}$ and enumerate $B=\{b_1,b_2,\ldots\}$. Each <injective function> $f:A\to B$ is determined by the finite tuple $(f(a_1),\ldots,f(a_m))$. Thus these functions form a subset of the finite <Cartesian product> $B^m$. A <finite Cartesian power of a countable set> is countable: for example, group the index tuples by the maximum of their coordinates, obtaining a <countable union of countable sets> consisting of finite groups.
There are also infinitely many such <injective functions>, since
$$
f_j(a_i)=b_{j+i}\qquad(j\geq0,\ 1\leq i\leq m)
$$
defines pairwise distinct examples. Therefore \b[$S_1$ is a <countably infinite set>].
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