# Set Theory/Zermelo-Fraenkel Axiomatic Set Theory

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## The axioms[edit]

- Extensionality, two sets with the same elements are equal.

- Separation, subsets exist

where*p*is any proposition

- The empty set exists

- Union, the union of all members of a set is a set.

- Power sets exist

we denote this set*y*by P(x)

- Infinity, an infinite set exists

- Foundation, no set is a member of itself