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

[tex]

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

[/itex]

I thought that this isomorphism would straightforwardly map an elementxonto-xin the second lattice, so why aren't these isomorphic please?

I see whythesetwo lattices aren't isomorphic:

[tex]

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

[/itex]

because the element0from the first one has no equivalent in the inversed lattice, but the first couple of lattices seems ok to me.

Thank you for clarification.

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# Why aren't these lattices isomorphic?

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