Finite Non-Empty Set

set-theory

Definition

Finite Non-Empty Set

A set $S$ is a finite non-empty set if it is finite and non-empty: there exists $n\in \mathbb{N}$, $n\ge 1$, and distinct elements $x_1,\dots ,x_n$ such that

$$S=\{x_1,\dots ,x_n\}.$$