Question

In both\(\mathbb Z\) and \(\mathbb R\)
1) if \(a,b\in S, a< b,~~then~~a\neq b\)
2)\(if ~~a 11 years ago

Answer 1

I 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?

Answer 2

On the other hand, if the relation is "less than", then, it works well for both set, hence they are isomorphic. Ha!!!!! I confused myself.

Answer 3

it must be one-to-one too right
and integers and reals have different cardinalities
idk what that means for present problem..

Answer 4

Modern geometry is my course. This is the very first section on the book and I got stuck everywhere. hihihi.....