Subset of Indiscrete Space is Sequentially Compact

Theorem
Let $T = \left({S, \left\{{\varnothing, S}\right\}}\right)$ be an indiscrete topological space.

Let $H \subseteq S$.

$H$ is sequentially compact in $T$.

Proof
From Convergent Sequences in Indiscrete Space, every sequence in $T$ converges to every point of $S$.

So every infinite sequence has a subsequence which converges to every point in $S$.

Hence $H$ is (trivially) sequentially compact in $T$.