Axiom of the Sum Set

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a of the sum (union) x of all sets that are elements of a. The axiom may be stated symbolically as

  exists x forall y(y in x= exists z in a(y in z)).

See also

Zermelo-Fraenkel Set Theory

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Itô, K. (Ed.). "Zermelo-Fraenkel Set Theory." §33B in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 1. Cambridge, MA: MIT Press, pp. 146-148, 1986.

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Axiom of the Sum Set

Cite this as:

Weisstein, Eric W. "Axiom of the Sum Set." From MathWorld--A Wolfram Web Resource.

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