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Hasse diagram of a POSET

  1. May 5, 2010 #1
    Ok I dont understand one thing...We ahd this example in school

    We have poset < {1,2,5,7,10,14,35,70}, | >
    | meas factor, for example a|b means b=ka, where k=integer

    and we got this Hasse diagram

    Code (Text):
            70
           / | \
         10 14 35
         | X  X |
         2   5  7
          \  | /
             1
    X means crossed lines

    But the hasse diagram definition says that we draw a line between element and the element above it if and only if the lower element is the immediate predecessor of the above one. So why is there a line between 1 and 5? Because theres element 2 in between. Same with 1 and 7, 2 and 10, 7 and 35, etc etc same with almost every element. To me they dont seem to be immediate predecessors/successors with each other

    I have google some more examples but they all have the same contradiction between definition and example. So what i dont understand here :(
     
    Last edited: May 5, 2010
  2. jcsd
  3. May 5, 2010 #2

    Hurkyl

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    Really? 1 divides 2 and 2 divides 5?
     
  4. May 5, 2010 #3
    i still dont get it :(
    for example why is 2 immediate predecessor of 10
     
    Last edited: May 5, 2010
  5. May 5, 2010 #4

    Hurkyl

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    Well, what could come between them? What numbers both divide 10 and are divisible by 2?
     
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