- #1
twoflower
- 368
- 0
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.
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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