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GLB and LUB

  1. May 23, 2012 #1
    The greatest lower bound and least upper bound of two elements a, b in a lattice do not have to be unique, do they? It could be the case that two equivalent or non-comparable glb or lub exist, right?
     
  2. jcsd
  3. May 23, 2012 #2
    They are unique in a lattice. By definition (according to wikipedia) a lattice a po-set where any two elements have a unique glb and lub (or infimum and supremum respectively).

    http://en.wikipedia.org/wiki/Lattice_(order [Broken])
     
    Last edited by a moderator: May 6, 2017
  4. May 23, 2012 #3
    Thanks.
     
  5. May 23, 2012 #4
    In a poset the glb and lub must be unique by antisymmetry.
     
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