**Proof by induction: For finite sets A, B w/ cardinality n, m >= 1, show there are...**

Let

*A*and

*B*be finite sets of cardinality

*n*and

*m*respectively, where

*n*and

*m*are positive natural numbers.

Show, using induction on

*n*, that there are

*m*functions from

^{n}*A*to

*B*.

Would i be ok to use base step as n = 1? for a function A -> B for one in A

A (x) mapping to B (a1,a2,a3.... am)

The number of functions possible for n-1 is m^n

I don't know how to go on with the induction step. Any ideas?

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