Power Set of Set of Finite Strings is Uncountable

Theorem
Let $\Sigma$ be a finite alphabet.

Let $\Sigma^*$ be the set of finite strings of $\Sigma$.

Let $\powerset {\Sigma^*}$ be the power set of $\Sigma^*$

Then $\powerset {\Sigma^*}$ is an uncountable set.

Proof
From Set of Finite Strings is Countably Infinite, $\Sigma^*$ is a countably infinite set.

The result follows from Power Set of Countably Infinite Set is Uncountable.