Definition:Enumeration/Countably Infinite

Definition

Let $X$ be a countably infinite set.

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

Notation

An infinite enumeration would usually be denoted either as:

Let $X = \set {x_1, x_2, \ldots}$

or:

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

Sources

• 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $2$. Set Theoretical Equivalence and Denumerability