Determine whether or not the set D of all functions f: ℤ_{+} ￫ ℤ_{+} is countable. Justify your answer.?
I have not been able to get anywhere with this problem. I would really appreciate any help with it.
Update:Yes, I do mean the positive integers.
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That's positive integers? As in N? If so, uncountable. Represent each function f as a sequence (f(1), f(2), f(3), ...) and use Cantor's diagonal argument from there.