Definition:Greatest Set by Set Inclusion/Class Theory

Definition
Let $\AA$ be a set of sets or a class of sets.

Then a set $M$ is the greatest element of $\AA$ (with respect to the subset relation) :


 * $M \in \AA$ and
 * $\forall S: \paren {S \in \AA \implies S \subseteq M}$

Also known as
Some sources use the term largest set. The two terms are synonymous.

Also see

 * Definition:Smallest Set