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25 March 2024
3 September 2023
RhubarbJayde
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RhubarbJayde
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..."
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