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Math Help - How can I show that these two semigroups is isomorphic?

  1. #1
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    Question How can I show that these two semigroups is isomorphic?

    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.
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  2. #2
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    Re: How can I show that these two semigroups is isomorphic?

    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.
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  3. #3
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    Re: How can I show that these two semigroups is isomorphic?

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