642 B
642 B
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Axioms of set theory
The basic notions of set theory are defined in Basic properties of sets. There we introduced a formal syntax that will be utilised to define the axioms. For easy reference:
- variables
a,b,c,...to range over sets - variables
x,y,zto range over ordinary objects as well as sets.
Axiom of Extensionality
Sets which contain the same members are the same set. If sets A and B contain the same elements then A = B.
\forall a \forall b [\forall x (x \in a \longleftrightarrow x \in b) \rightarrow a =b]