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

[tomboi03]

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?

 

[phreak]

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'.