Exercise 219Logic, sets and proofs › Countability and cardinalityHigh schoolAdded 3 Nov 2026

$\mathbb{N}$ is countably infinite

#naturals#countably infinite#identity

Statement

Show that $\mathbb{N}$ is countably infinite.

Hint

The identity map is a bijection $\mathbb{N}\to\mathbb{N}$ .

Show solutionHide solution

Bijection. $\mathrm{id}:\mathbb{N}\to\mathbb{N}$ is trivially a bijection.

Conclusion. $|\mathbb{N}|=\aleph_0$ .