Category:Set Equality

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This category contains results about Set Equality.
Definitions specific to this category can be found in Definitions/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 $T$


$T$ is a subset of $S$


This category has only the following subcategory.