Category:Definitions/Set Equality

This category contains definitions related to Set Equality.
Related results can be found in Category:Set Equality.

Let $S$ and $T$ be sets.

Definition 1

$S$ and $T$ are equal if and only if they have the same elements:

$S = T \iff \paren {\forall x: x \in S \iff x \in T}$

Definition 2

$S$ and $T$ are equal if and only if both:

$S$ is a subset of $T$

and

$T$ is a subset of $S$