Definition·D005
Power set
The set of all subsets of A.
where
is subset.
In words
x belongs to the power set of A exactly when x is a subset of A.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
The power set
, the collection of all subsets of
. Its existence for every set
is guaranteed by the power set axiom A04.
Used by
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