ThmDex – An index of mathematical definitions, results, and conjectures.

Result R511 on D16: Countable set
Subresult of R5076: Bijection from the natural number plane to the set of natural numbers

Natural number plane is countable

Formulation 0

Let $\mathbb{N}$ be the D225: Set of natural numbers such that

(i)	$\mathbb{N} \times \mathbb{N}$ is a D191: Binary cartesian set product for $(\mathbb{N}, \mathbb{N})$

Then $\mathbb{N} \times \mathbb{N}$ is a D16: Countable set.

Proofs

Proof 0

Let $\mathbb{N}$ be the D225: Set of natural numbers such that

(i)	$\mathbb{N} \times \mathbb{N}$ is a D191: Binary cartesian set product for $(\mathbb{N}, \mathbb{N})$