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Math Help - Integer - upper bounds

  1. #1
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    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 \bar{S} has no upper bound.

    ( \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!
    Last edited by WWTL@WHL; November 16th 2007 at 10:51 AM.
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  2. #2
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    Quote Originally Posted by WWTL@WHL View Post
    Hey fellas, I'm stuck on this question.

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

    ( \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!
    S=\{1\}
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    S=\{1\}
    Bah! Sorry, I copied it down wrong. It's edited now.
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  4. #4
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    If M is an upper bound for S then for each positive integer k, M+k is not in S.
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  5. #5
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    Quote Originally Posted by Plato View Post
    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.
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