Definition:Non-Empty Set

Definition
Let $S$ be a set.

Then $S$ is said to be non-empty $S$ has at least one element.

By the Axiom of Extension, this may also be phrased as:


 * $S \ne \varnothing$

where $\varnothing$ denotes the empty set.

Many mathematical theorems and definitions require sets to be non-empty in order to avoid erratic results and inconsistencies.

Also known as
Some sources prefer to use nonempty, but, in striving for consistency, standardises on non-empty.

Also see

 * Definition:Empty Set