# Definition:Smallest Set by Set Inclusion/Class Theory

## Definition

Let $A$ be a class.

Then a set $m$ is the smallest element of $A$ (with respect to the inclusion relation) if and only if:

$(1): \quad m \in A$
$(2): \quad \forall S: \paren {S \in A \implies m \subseteq S}$

## Also known as

The smallest element in this context is also referred to as the least element.