# Definition:Greatest/Set

< Definition:Greatest(Redirected from Definition:Greatest Set)

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## Contents

## 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) if and only if:

- $M \in \AA$ 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

## Sources

2010: Raymond M. Smullyan and Melvin Fitting: *Set Theory and the Continuum Problem* (revised ed.): Definition $3.4.8$