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Why aren't these lattices isomorphic?

  1. Dec 20, 2006 #1

    I can't see why these lattices aren't isomorphic:

    (\mathbb{N} \mbox{ u } \left\{-\infty, +\infty\right\}, \le) \mbox{ and } (\mathbb{N} \mbox{ u } \left\{-\infty, +\infty\right\}, \le)^{inverse}

    I thought that this isomorphism would straightforwardly map an element x onto -x in the second lattice, so why aren't these isomorphic please?

    I see why these two lattices aren't isomorphic:

    (\mathbb{N}, \le) \mbox{ and } (\mathbb{N}, \le)^{inverse}

    because the element 0 from the first one has no equivalent in the inversed lattice, but the first couple of lattices seems ok to me.

    Thank you for clarification.
    Last edited: Dec 20, 2006
  2. jcsd
  3. Dec 20, 2006 #2


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    Homework Helper

    N consists only of positive integers. If you meant Z, all integers, the first pair are isomorphic.
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