Consequences
The Power Set Axiom allows a simple definition of the Cartesian product of two sets and :
Notice that
and thus the Cartesian product is a set since
One may define the Cartesian product of any finite collection of sets recursively:
Note that the existence of the Cartesian product can be proved without using the power set axiom, as in the case of the Kripke–Platek set theory.
Read more about this topic: Axiom Of Power Set
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