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

Cardinals · Naive Set Theory