Power set
Revision as of 20:10, 26 August 2006 by Boy Soprano II (talk | contribs)
The power set of a given set is the set
of subsets of that set.
The empty set has only one subset, itself. Thus .
A set with a single element has two subsets, the empty set and the entire set. Thus
.
A set with two elements has four subsets, and
.
Similarly, for any finite set with elements, the power set has
elements.
Note that for any set such that
,
, so the power set of any set
has a cardinality at least as large as that of
itself.
Proof
See Also
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