Axiom of the Unordered Pair

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any sets a and b of a set x having a and b as its only elements. x is called the unordered pair of a and b, denoted {a,b}. The axiom may be stated symbolically as

  exists x forall y(y in x=y=a v y=b).

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 Unordered Pair

Cite this as:

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

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