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 subset relation) :


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

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

Also see

 * Definition:Greatest Set by Set Inclusion (Class Theory)