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WAPower set

Axiom·A04

The collection of all subsets of a set is itself a set.

Here is subset, and is the power set of D005.
In words
For any set A, there is a set P where for every x, x belongs to P exactly when x is a subset of A.
This is a ZFC axiom: it is assumed, not proven. Everything below it in a proof chain ultimately rests here.

Remarks

Guarantees the power set of D005 exists for every set . This is the source of the towering hierarchy of ever larger sets and the engine of cardinal comparison: Cantor's theorem shows is always strictly larger than .
Wikipedia ↗Set.powerset ↗

Used by

T03T17T21
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