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The '''Axiom of Foundation''' is the most recent of the [[axiom]]s of [[Zermelo-Fraenkel]] set theory to be added to the list. It states that for every set ''A'' the sequence:
The '''Axiom of Foundation''' is the most recent of the [[axiom]]s of [[Zermelo-Fraenkel]] set theory to be added to the list. It states that for every set ''A'' the sequence:
* ''A''
* ''A''
* elements of ''A''
* ''A<sub>1</sub>'' an element of ''A''
* elemenents of elements of ''A''
* ''A<sub>2</sub>'' an element of ''A<sub>1</sub>''
* elemenets of elements of elemeents of ''A''
* ''A<sub>3</sub>'' an element of ''A<sub>2</sub>''
* etc.
* etc.