Difference between revisions of "Power set"
From Maths
m |
m |
||
| Line 4: | Line 4: | ||
The characteristic property of the power set is that <math>\forall U\subset X:U\in\mathcal{P}(X)</math> | The characteristic property of the power set is that <math>\forall U\subset X:U\in\mathcal{P}(X)</math> | ||
| − | It is the set of all subsets of | + | It is the set of all subsets of <math>X</math> |
{{Definition}} | {{Definition}} | ||
Revision as of 18:48, 12 February 2015
The power set of a set X is denoted by P(X), sometimes 2X (a number to the power of a set is not defined (as it cannot be usefully defined) leaving it free to be used as notation. This comes from the cardinality of the power set being 2|X|)
The characteristic property of the power set is that ∀U⊂X:U∈P(X)
It is the set of all subsets of X
