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Loser66
 one year ago
In both\(\mathbb Z\) and \(\mathbb R\)
1) if \(a,b\in S, a< b,~~then~~a\neq b\)
2)\(if ~~a<b~~and~~b<c,~~then~~a<c\)
Do they isomorphic ? (in Z and in R)
Please, help.
Loser66
 one year ago
In both\(\mathbb Z\) and \(\mathbb R\) 1) if \(a,b\in S, a< b,~~then~~a\neq b\) 2)\(if ~~a<b~~and~~b<c,~~then~~a<c\) Do they isomorphic ? (in Z and in R) Please, help.

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I feel like they are not one to one but don't know how. I establish \(f:\mathbb Z\rightarrow \mathbb R\) , \(f: (a,b)\mapsto a/b\) I can see that f is not one to one. But how to put this logic into the problem?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0On the other hand, if the relation is "less than", then, it works well for both set, hence they are isomorphic. Ha!!!!! I confused myself.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0it must be onetoone too right and integers and reals have different cardinalities idk what that means for present problem..

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Modern geometry is my course. This is the very first section on the book and I got stuck everywhere. hihihi.....
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