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Thread: 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 $\displaystyle A\subset X$ is defined as number $\displaystyle x_0\in X$ with the property $\displaystyle x_0\leq a$ for all $\displaystyle a\in A$. It may be that $\displaystyle x_0$ in $\displaystyle A$, but it doesn't have to be. If $\displaystyle x_0\in A$ is a lower bound then it is automatically "the biggest lowerbound". Then $\displaystyle x_0$ is called a minimum of $\displaystyle A$.

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