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:


 * $S \ne \O$

where $\O$ denotes the empty set.

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

Non-Empty Class
In the context of class theory, the definition follows the same lines:

Also see

 * Definition:Empty Set