Set Theory/Zermelo-Fraenkel Axiomatic Set Theory

< Set Theory

The axiomsEdit

  • 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