Cantor's Diagonal Argument/Examples
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Examples of Use of Cantor's Diagonal Argument
Set of Mappings from Integers to Boolean Set is Uncountable
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.