- #1

- 368

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Hi,

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 element

I see why

[tex]

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

[/itex]

because the element

Thank you for clarification.

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 element

**x**onto**-x**in the second lattice, so why aren't these isomorphic please?I see why

**these**two lattices aren't isomorphic:[tex]

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

[/itex]

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.

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