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Mathematics
Set Theory, Logic, Probability, Statistics
Why is the Axiom of Power Set needed?
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[QUOTE="fresh_42, post: 6041957, member: 572553"] Definitions are only names. They do not have any other function than to support language and abbreviate it. Axioms are rules. They determine whether a conclusion is allowed or not. Why does a power set exist at all? Do you know a derivation from the other axioms? If it was a definition, then it would read: "A set with this and that property is called a power set." As an Axiom, the existence of such a set is required: "There is a power set." So the axiom frees you from the need to construct one, which would be rather difficult for let's say ##x=\mathbb{R}\,.## [/QUOTE]
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Why is the Axiom of Power Set needed?
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