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Mathematics
Set Theory, Logic, Probability, Statistics
Why is the Axiom of Power Set needed?
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[QUOTE="member 587159, post: 6041980"] You can only define objects that already exist. As an easy example, we can define ##\sqrt{x}## for ##x \geq 0## as the unique number ##y \geq 0## with ##y^2 =x##. But who says that such a number ##y## exists? And that it is unique? These things have to be verified (and any proof will somehow invoke the LUB property), or the definition wouldn't make sense. For the same reason, before we define what the term "power set" means, we have to verify if that object exists. Since we can't deduce the existence of the power set from the other ZFC axioms, it is added as an axiom. [/QUOTE]
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Why is the Axiom of Power Set needed?
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