Category:Class Union

From ProofWiki
Jump to navigation Jump to search

This category contains results about Class Union.
Definitions specific to this category can be found in Definitions/Class Union.

Let $A$ and $B$ be two classes.

The (class) union $A \cup B$ of $A$ and $B$ is defined as the class of all sets $x$ such that either $x \in A$ or $x \in B$ or both:

$x \in A \cup B \iff x \in A \lor x \in B$


$A \cup B = \set {x: x \in A \lor x \in B}$

General Definition

Let $A$ be a class.

The union of $A$ is:

$\bigcup A := \set {x: \exists y: x \in y \land y \in A}$

That is, the class of all elements of all elements of $A$ which are themselves sets.