Definition:Enumeration/Countably Infinite

Definition
Let $X$ be a countably infinite set.

An enumeration of $X$ is a bijection $x: \N \to X$.

It is common to denote an (infinite) enumeration by writing, for example:


 * Let $X = \set {x_1, x_2, \ldots}$ [...]

or:


 * Let $x_1, x_2, \ldots$ be an enumeration of $X$. [...]