Definition:Class Union

Definition

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:

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

or:

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

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.

Also see

• Definition:Set Union, the usual presentation of this concept in set theory

• Definition:Class Intersection

• Results about class unions can be found here.

Internationalization

Union is translated:

In French:	somme	(literally: sum)
In French:	union
In French:	réunion
In Dutch:	vereniging

Sources

• 2002: Thomas Jech: Set Theory (3rd ed.) ... (previous) ... (next): Chapter $1$: Classes
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 5$ The union axiom: Boolean operations $(1)$