There are m functions from a one-element set to the set 1


Question: There are m functions from a one-element set to the set {1, 2,...,m}. How many functions are there from a two-element set to {1, 2,...,m}? From a three-element set? Give a recurrence for the number T(n) of functions from an n-element set to {1, 2,...,m}. Solve the recurrence.

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Mathematics: There are m functions from a one-element set to the set 1
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