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Axiom of the Empty Set


The axiom of the empty set asserts the existence of a set with no elements, the empty set emptyset. It is one of the Zermelo-Fraenkel axioms and may be stated symbolically as

  exists x forall y(y not in x).

Here  exists is the existential quantifier ("there exists"),  forall is the universal quantifier ("for every"), and y not in x means that y is not an element of x.


See also

Zermelo-Fraenkel Axioms

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References

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.

Referenced on Wolfram|Alpha

Axiom of the Empty Set

Cite this as:

Weisstein, Eric W. "Axiom of the Empty Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AxiomoftheEmptySet.html

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