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Math Help - Point set proof

  1. #1
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    Help with point set proof

    Show that if M is a point set and there is a point p which is the first point to the right of M, then p is a limit point of M.

    Definition: If M is a point set and p is a point, the statement that p is a limit point of the point set M means that every open interval containing p contains a point of M different from p.

    Definition: P is the first point to the right of the point set M means that p is greater than every point of M and if q is a point less than p, then q is not greater than every point of M.

    Axiom: If p and q are two distinct points then there is a point between them, for example, (p+q)/2.
    Last edited by spikedpunch; September 14th 2009 at 12:30 PM. Reason: Added def's and axiom
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  2. #2
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    Quote Originally Posted by spikedpunch View Post
    Help please!
    Show that if M is a point set and there is a point p which is the first point to the right of M, then p is a limit point of M.
    We really cannot help you unless you give us a lot more information about the axioms and definitions used in your course. If I had to guess, I would say that this is from a set of notes based on class notes given a long time ago by R L Moore or one of his students.
    For example: What does the first point to the right of M mean?
    If my guess is correct, then it would imply that each region that contains p must contain a point of M distinct from p. Otherwise p would not be the first point to the right of M. That is enough to make p a limit point of M.

    But you see that is just a wild guess as to what the terms mean.
    So you are going to have to fill a great many more details to get any meaningful help.
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  3. #3
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    Added definitions and axiom
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  4. #4
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    Quote Originally Posted by spikedpunch View Post
    Added definitions and axiom
    Region equals open interval.
    Then the outlined proof I gave above works.
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