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Why is it that we denote the set of all subsets of $A$ by $2^A$?

Is there any historical or logical cause that motivated this notation?

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    @Rahul Interesting.2012-04-11

2 Answers 2

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Another reason is that the set of all subsets of $A$ can be identified with all functions $A\to \{0,1\}$ and $\{0,1\}$ is sometimes called $2$. Plus the common usage of $B^A$ to denote the set of all functions $A\to B$.

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    @jwodder Thanks!2012-04-11
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Motivation: the cardinality is $2^{|A|}$.