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

# Axiom of the Unordered Pair

## See also

Zermelo-Fraenkel Set Theory## Explore with Wolfram|Alpha

## 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 Unordered Pair## Cite this as:

Weisstein, Eric W. "Axiom of the Unordered
Pair." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AxiomoftheUnorderedPair.html