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[topology] order, intervals

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data
    It might not be a real topology question, but it's an exercise question in the topology course I'm taking. The question is not too hard, but I'm mainly doubting about the terminology:
    2. Relevant equations
    N.A.

    3. The attempt at a solution
    I would think not, unless I'm misunderstanding the terminology. Take the rational numbers and the subset denoted in [itex]\mathbb R[/itex] as [itex][\sqrt{2},2] \cap \mathbb Q[/itex]. It is indeed convex in [itex]\mathbb Q[/itex], but it's not an interval, cause I can't write it as [itex][q_1,q_2][/itex] or [itex]]q_1,q_2][/itex] with [itex]q_i \in \mathbb Q[/itex], or is my notion of interval too narrow?
     
  2. jcsd
  3. Feb 1, 2012 #2

    tiny-tim

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    hi mr. vodka! :smile:

    doesn't "convex" mean that, between any two elements of Y, there's no element in X that isn't in Y ?
     
  4. Feb 1, 2012 #3
    Uhu. Which is true if you view that set as a part of the rational numbers, right?
     
  5. Feb 1, 2012 #4
    How is that in Q?
     
  6. Feb 1, 2012 #5

    tiny-tim

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    oops! :redface: misread the question! :rolleyes:

    let me start again …

    √2 isn't in Q, so what's the meaning of [itex][\sqrt{2},2] \cap \mathbb Q[/itex] ? :confused:
     
  7. Feb 1, 2012 #6
    Well you know what it means in R, right? And then you can interpret it as a subset of Q.
     
  8. Feb 1, 2012 #7

    HallsofIvy

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    Well, [itex][-\sqrt{2},\sqrt{2}][/itex] as a subset of R is not the same set as [itex][-\sqrt{2}, \sqrt{2}][/itex] as a subset of Q. The first contains many points not in the second.
     
  9. Feb 1, 2012 #8
    but that's not the subset I regarded, I regarded the intersection with Q
     
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