Definition. Countable sets [dm-0009]

Liam O'Connor

A set $X$ is countable if it can be put into a one-to-one correspondence with the natural numbers $\mathbb {N}$ .

Backlinks

Definition. $\omega$ -chain [dt-000W]

Liam O'Connor

An $\omega$ -chain is a chain that is countable. In other words, it is a sequence of elements $x_{i \in \mathbb {N}}$ such that: $x_0 \sqsubseteq x_1 \sqsubseteq x_2 \sqsubseteq x_3 \dots$

Related

Definition. Set bijection [dm-000A]

Liam O'Connor

A bijection between sets $A$ and $B$ is a one to one correspondence between their elements. That is, $R \subseteq A \times B$ is a bijection between $A$ and $B$ if, for each $x \in A$ , there is exactly one $y \in B$ such that $x\ R\ y$ , and vice versa.