Definition:Class Union/General Definition
< Definition:Class Union(Redirected from Definition:Union of Class)
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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 denoted as
Some sources denote $\bigcup A$ as $\ds \bigcup_{x \mathop \in A} x$.
Also see
- Results about class union can be found here.
Sources
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 5.5$
- 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