Limit Points of Sequence in Indiscrete Space on Uncountable Set

Theorem
Let $S$ be an uncountable set.

Let $T = \struct {S, \set {\O, S} }$ be the indiscrete topological space on $S$.

Let $\sequence {s_n}$ be a sequence in $T$.

Then every sequence in $T$ has an uncountable number of limits.

Proof
From Sequence in Indiscrete Space converges to Every Point, $\sequence {s_n}$ converges to every point of $S$.

As $S$ is uncountable, the result follows.