Axiom of the Empty Set

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as

  exists x forall y(!y in x).

See also

Zermelo-Fraenkel Axioms

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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 Empty Set

Cite this as:

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

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