# Why aren't these lattices isomorphic?

1. Dec 20, 2006

### twoflower

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 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.

Last edited: Dec 20, 2006
2. Dec 20, 2006

### StatusX

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