Difference between revisions of "Power set"
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| − | The power set of a a | + | The power set of a set <math>X</math> is denoted by <math>\mathcal{P}(X)</math>, sometimes <math>2^X</math> (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|cardinality]] of the power set being <math>2^{|X|}</math>) |
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| + | The characteristic property of the power set is that <math>\forall U\subset X:U\in\mathcal{P}(X)</math> | ||
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| + | It is the set of all subsets of <math>X</math> | ||
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| + | {{Definition}} | ||
Latest revision as of 16:30, 23 August 2015
The power set of a set [math]X[/math] is denoted by [math]\mathcal{P}(X)[/math], sometimes [math]2^X[/math] (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 [math]2^{|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 [math]X[/math]
