Bound on Natural Numbers proof

• November 15th 2010, 09:57 AM
jstarks44444
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
• November 15th 2010, 10:13 AM
roninpro
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?
• November 17th 2010, 09:16 AM
jstarks44444
Well, isn't the upper bound $a_k$ there? What do you mean by forward direction?