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1. The problem statement, all variables and given/known data

Suppose we found a 1-to-1 function k that maps the set A to the set N, where N is the set of natural numbers. What can we say about the set A?

2. Relevant equations

3. The attempt at a solution

The answer is 'A is at most countable.' I understand this. But my question is, is it also possible for A to be finite, as well as infinite? i.e. its possible for A to be either

{a1, a2, a3}

or

{a1, a2, a3, a4, a5,...}

all the way to infinity.

Thanks,

M

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# Homework Help: Countable sets | If k:A->N is 1-to-1, then A is

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