Power set
In mathematics , the power set of a set S , written as
P
(
S
)
{\displaystyle P(S)}
or
P
(
S
)
{\displaystyle {\mathcal {P}(S)}
,[1] is the set of all subsets of S. In terms of cardinality , a power set is larger than the set it originates from. If S is a finite set with n elements, then
P
(
S
)
{\displaystyle P(S)}
would have
2
n
{\displaystyle 2^{n}
elements.[2] [3]
Examples
The power set of
{
2
,
5
}
{\displaystyle \{2,5\}
is
{
{
}
,
{
2
}
,
{
5
}
,
{
2
,
5
}
}
{\displaystyle \{\{\},\{2\},\{5\},\{2,5\}\}
.
The power set of
{
3
,
4
,
10
}
{\displaystyle \{3,4,10\}
is
{
{
}
,
{
3
}
,
{
4
}
,
{
10
}
,
{
3
,
4
}
,
{
3
,
10
}
,
{
4
,
10
}
,
{
3
,
4
,
10
}
}
{\displaystyle \{\{\},\{3\},\{4\},\{10\},\{3,4\},\{3,10\},\{4,10\},\{3,4,10\}\}
.
Related pages
References
↑ "Comprehensive List of Set Theory Symbols" . Math Vault . 2020-04-11. Retrieved 2020-09-05 .
↑ Weisstein, Eric W. "Power Set" . mathworld.wolfram.com . Retrieved 2020-09-05 .
↑ "Power Set" . www.mathsisfun.com . Retrieved 2020-09-05 .
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