# Thread: Integer - upper bounds

1. ## Integer - upper bounds

Hey fellas, I'm stuck on this question.

Question:
Prove that, if S is a set of integers with an upper bound, then $\displaystyle \bar{S}$ has no upper bound.

($\displaystyle \bar{S}$ is the set where x is an integer such that x does not belong to the set S - i.e. everything not in S, I'm guessing)

I would provide an attempt, but I really have no clue. Any ideas?

Thanks a bunch, guys!

2. Originally Posted by WWTL@WHL
Hey fellas, I'm stuck on this question.

Question:
Prove that, if S is a set of integers with an upper bound, then $\displaystyle \bar{S}$ has an upper bound.

($\displaystyle \bar{S}$ is the set where x is an integer such that x does not belong to the set S - i.e. everything not in S, I'm guessing)

I would provide an attempt, but I really have no clue. Any ideas?

Thanks a bunch, guys!
$\displaystyle S=\{1\}$

3. Originally Posted by ThePerfectHacker
$\displaystyle S=\{1\}$
Bah! Sorry, I copied it down wrong. It's edited now.

4. If M is an upper bound for S then for each positive integer k, M+k is not in S.

5. Originally Posted by Plato
If M is an upper bound for S then for each positive integer k, M+k is not in S.
Hmm, I guess it really must be that simple. I was thinking of doing that a while back, but I was worried it wouldn't be formal enough.

Thanks Plato.