I have this problem to solve but I cant get my head wrapped arround it. Most of the tutorials keeps showing example of proving that there is uncountable number of binary functions. I have following problem...

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

Can someone give me some pointers or guide me a little to solve this problem please. I would prefer guidance over the solution becuase i need to know how to solve these kinds of problems using diagonalization.