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Math Help - Hasse Diagram - lower upper bound

  1. #16
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    {a,c,d,f} upper bounds - f,h and j
    my question - why include "f" in upper bound?
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  2. #17
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by robocop_911 View Post
    {a,c,d,f} upper bounds - f,h and j
    my question - why include "f" in upper bound?
    try understanding the definition like what plato said..
    post the definition you have and point us what you dont understand on the statement..
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  3. #18
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by robocop_911 View Post
    1) {b,d,g} upper bounds - g and h
    my question - why not only "h" why include g in it?
    Because both succeed every term in {b,d,g}. Don’t forget that partial orders are reflexive, therefore (g,g).
    Then how come upper bounds of {a,b,c} is e,f,j and h and not something like c,e,f,j,h? (c,c) (b,b) that's also reflexive!
    because, they are not connected to all of a,b and c..
    Quote Originally Posted by robocop_911 View Post
    2) {b,d,g} least upper bound - g
    my question - How come it is "g" why not "h" since h>g
    Because there is only one LUB for any given set and g is the first or least.

    So least upper bound should be from the set given only right?
    not all the time..
    Quote Originally Posted by robocop_911 View Post
    In this case it is {b,d,g} so here it is "b". Is it also the greatest lower bound?
    yes, you are right..
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