In computer science, an alphabet is a finite non-empty set.

Every free action on a non-empty set is faithful.

The others have a form that partitions all numbers from previous generations into two non-empty sets.

This, in particular, shows that for any non-empty set, there is always a metric space associated to it.

Informally it states that one can simultaneously choose an element from every non-empty set.

It is also easy to see that every non-empty set in is infinite.

In the category of non-empty sets, there are no initial objects.

Let X be a non-empty set and G a group.

It states that any countable collection of non-empty sets must have a choice function.

AC states that every collection of non-empty sets must have a choice function.