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• 17:17, 3 September 2023 RhubarbJayde talk contribs created page Powerset (Created page with "The powerset of a set \(X\), denoted \(\mathcal{P}(X)\), is the collection of all subsets of \(X\). It is easy to see that, for \(X\) finite, the powerset of \(X\) has cardinality \(2^{|X|}\), and the same fact holds when \(X\) is infinite, although this is because cardinal arithmetic was defined to have that behaviour. Cantor's diagonal argument proves that the powerset of the natural numbers, \(\mathcal{P}(\mathbb{N})\), is uncountable. The questi...") Tag: Visual edit