Question: (20) (a) A function f from N to N is an increasing function if i < j, then f(i) < f(j). Prove, using the

(20) (a) A function f from N to N is an increasing function if i < j, then f(i) < f(j). Prove, using the technique of diagonalization, that there are uncountable number of increas- ing functions from N to N; (b) Show that the set of all functions from N to {5i|i N} is uncountable.

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