Why is P(A) called the power set of A?

tomboi03
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Why is P(A) called the power set of A?

I don't know what to say about this... can you explain this to me?
 
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This is just a guess, but if |A| denotes the cardinality of A, then |P(A)| = 2^A, which may have led to the name 'power set'.
 

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