# Math Help - Bound on Natural Numbers proof

1. ## Bound 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

2. How about the forward direction first?

Suppose that $A\subset \mathbb{N}$ is finite. We can write it as $A=\{a_1, a_2,\ldots, a_k\}$. Can you find an upper bound for this set?

3. Well, isn't the upper bound $a_k$ there? What do you mean by forward direction?