Hey all, I would really appreciate some help with this question. The proposition to be proved:

A nonempty subset of N (the natural numbers) is finite if and only if it is bounded above.

How would one go about proving this? Thanks a bunch

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- Nov 15th 2010, 08:57 AMjstarks44444Bound on Natural Numbers proof
Hey all, I would really appreciate some help with this question. The proposition to be proved:

A nonempty subset of N (the natural numbers) is finite if and only if it is bounded above.

How would one go about proving this? Thanks a bunch - Nov 15th 2010, 09:13 AMroninpro
How about the forward direction first?

Suppose that $\displaystyle A\subset \mathbb{N}$ is finite. We can write it as $\displaystyle A=\{a_1, a_2,\ldots, a_k\}$. Can you find an upper bound for this set? - Nov 17th 2010, 08:16 AMjstarks44444
Well, isn't the upper bound $\displaystyle a_k$ there? What do you mean by forward direction?