Category:Examples of Use of Cantor's Diagonal Argument

This category contains examples of use of Cantor's Diagonal Argument.

Let $S$ be a set such that $\card S > 1$, that is, such that $S$ is not a singleton.

Let $\mathbb F$ be the set of all mappings from the natural numbers $\N$ to $S$:

$\mathbb F = \set {f: \N \to S}$

Then $\mathbb F$ is uncountably infinite.