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Set Sizes (Continued)

Proposition: If A and B have size m and n, respectively, then the size of the set of functions from A to B is nm:

forall A, B, m in N, n in N:
   (|A| = m /\  |B| = n) => |A -> B| = nm.

If A is of size n, then A has 2n subsets:

forall A, n in N:
   |A| = n => |P(A)| = 2n.

Author: Wolfgang Schreiner
Last Modification: December 7, 1999

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