- #1
pellman
- 684
- 5
In the Zermelo-Fraenkel axioms of axiomatic set theory we find:
Axiom. Given any set x, there is a set
such that, given any set z, this set z is a member of
if and only if every element of z is also an element of x.
Why is this needed as an axiom? why isn't it merely a definition? Under what situation would the existence of the power set be in question? seems like it can always be constructed.
Axiom. Given any set x, there is a set
Why is this needed as an axiom? why isn't it merely a definition? Under what situation would the existence of the power set be in question? seems like it can always be constructed.