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Math Help - Simple question on sets and bounds... dont laugh :p

  1. #1
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    Simple question on sets and bounds... dont laugh :p

    On Upper and lower bounds - Wikipedia, the free encyclopedia
    it says "2 and 5 are both lower bounds for the set { 5, 10, 34, 13934}"
    how is 2 a lower bound when it is not even in the set?

    thanks in advance
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  2. #2
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    You can construct 2

    10/5 is 2 but u cant construct any lower whole number, prehaps thats what they tried to express..
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  3. #3
    Senior Member Dinkydoe's Avatar
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    A lower bound for a set A\subset X is defined as number x_0\in X with the property x_0\leq a for all a\in A. It may be that x_0 in A, but it doesn't have to be. If x_0\in A is a lower bound then it is automatically "the biggest lowerbound". Then x_0 is called a minimum of A.

    If we look at your example, where we look at the given set as a subset A\subset\mathbb{N}. Then x_0= 2, x_0= 5 are both lower bounds. They satisfy x_0\leq a for all a\in A. Even better x_0 = 2 is a minimum of A.
    Last edited by Dinkydoe; January 30th 2010 at 04:12 AM.
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