Axiom of Replacement

One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of a set x such that, for any y of a, if there exists a z satisfying A(y,z), then such z exists in x,

  exists x forall y in a( exists zA(y,z)=> exists z in xA(y,z)).

This axiom was introduced by Fraenkel.

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.

Referenced on Wolfram|Alpha

Axiom of Replacement

Cite this as:

Weisstein, Eric W. "Axiom of Replacement." From MathWorld--A Wolfram Web Resource.

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