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Math Help - Bound on Natural Numbers proof

  1. #1
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    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
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  2. #2
    Senior Member roninpro's Avatar
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    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?
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  3. #3
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    Well, isn't the upper bound a_k there? What do you mean by forward direction?
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