define the following map:
f(x) = ex.
prove f is a semi-group homomorphism (it's actually a MONOID homomorphism).
then, prove f is bijective.
I have these two semigroups (ℝ≥0, +) and (ℝ≥1, *) where * is multiplication.
How can I show that these are isomorphic?
I know from wikipedia that:
"Two semigroups S and T are said to be isomorphic if there is a bijection f : S ↔ T with the property that, for any elements a, b in S, f(ab) = f(a)f(b). Isomorphic semigroups have the same structure."
But I have no idea on how to go about proving this. Any help would be highly appreciated.