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Thread: Set Help

  1. #1
    Newbie
    Joined
    Oct 2009
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    5

    Set Help

    Give an example of a linearly ordered set (L,<) and an initial segment S of L which is not of the form {x | x<a}, for any a in L.

    Any suggestions?
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Paris
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    There is an important difference between $\displaystyle \mathbb{Q}$ and $\displaystyle \mathbb{R}$ that allows you to find initial segments of $\displaystyle \mathbb{Q}$ you cannot write $\displaystyle \{x\in\mathbb{Q}\ ;\ x<a\}$ for any $\displaystyle a\in \mathbb{Q}$.


    An example different from the ones you get with the remark: $\displaystyle [-\infty ,0]\subset\mathbb{R}$.
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