Set of Mappings from Integers to Boolean Set is Uncountable

Example of Use of Cantor's Diagonal Argument
Let $S$ be the Boolean set defined as:
 * $S = \set {0, 1}$

Let $\mathbb G$ be the set of all mappings from the integers $\Z$ to $S$:
 * $\mathbb G = \set {f: \Z \to S}$

Then $\mathbb G$ is uncountably infinite.

Proof
This is an instance of the corollary to Cantor's Diagonal Argument.