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What does this symbol even mean?

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Show for any metric space (S,d) and  e> 0 that N(e, S) <=  D(e, S) <= N(e/2, S)


    2. Relevant equations
    none

    3. The attempt at a solution
    Can somebody please tell me what does N(e,S) or D(e,S) even mean so I can at least know what I am asked to prove?

    I dig through all the notes, and online sources and could not find anything operation that involves a metric space with a real number.

    Thanks!
     
  2. jcsd
  3. Oct 5, 2011 #2

    Mark44

    Staff: Mentor

    My browser (IE 8) shows empty boxes for six of the symbols above.

    Do you have a textbook? If so, it should define any notation like this that is used. N(. , .) could mean "neighborhood", but the notation used in the text I studied for my Topology class uses N(p, ε) to mean the ε-neighborhood of a point p in set S.
     
  4. Oct 5, 2011 #3
    Mark...don't use Internet Explorer. This is 2011, use Mozilla FireFox.
     
  5. Oct 5, 2011 #4

    phinds

    User Avatar
    Gold Member
    2016 Award

    FireFox is pure crap for a lot of operations, so some of us shun it. For the casual user it seems OK but if you are a software developer, it is useless.
     
  6. Oct 5, 2011 #5
    Use Chrome then?
     
  7. Oct 5, 2011 #6
    Uh they are just all regular texts. Thanks for your help, I suspected it meaning neighborhood too, you see, neighborhood is defined by a point and a positive number. Here it is just a metric space and a positive number, what kind of things can be defined out of this?

    And this class doesn't have a textbook. We use only a power point slide, which I look through at least 10 times and found nothing that relates to this.

    It feels one way when you don't know how to prove a statement, but it feels totally different when you don't even know what statement you are asked to prove.
     
  8. Oct 5, 2011 #7

    Mark44

    Staff: Mentor

    Unless someone else here can decipher this, you should ask your instructor what the notation means.
     
  9. Oct 5, 2011 #8
    If there was time I would't be here. Oh well..... it's life. It's funny how the instructor just put it there as if it a commonly used notation
     
  10. Oct 5, 2011 #9
  11. Oct 5, 2011 #10
    What was the symbol? Was it X?
     
  12. Oct 5, 2011 #11
    Symbols here <==> Symbols in the link [p]
    S X
    d rho
    N N
    D M
     
  13. Oct 5, 2011 #12
    <=> is if and only if
     
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