Question: I will need the prove for both repeating and non-repeating cases. 21. A total function f from N to N is said to be repeating

I will need the prove for both repeating and non-repeating cases.  I will need the prove for both repeating and non-repeating cases.

21. A total function f from N to N is said to be repeating if f(n)= f(n + 1) for some ne N. Otherwise, f is said to be nonrepeating. Prove that there are an uncountable number of repeating functions. Also prove that there are an uncountable number of nonrepeating functions

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