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Reals under multiplication homomorphisms

  1. Jul 16, 2007 #1
    1. The problem statement, all variables and given/known data
    A function f:R-->R^x is a homomorphism iff f(x+y) = f(x) + f(y) for all x,y in R


    2. Relevant equations

    I dont know what group R^x is. I can only assume it means Reals under multiplication . Would that mean that f(x+y) = f(x)f(y)? How does the function work? Since 5 is in R what would it be mapped to in t R^x?


    3. The attempt at a solution

    This isnt a homework question, I read it in the book as a false statement but there was no explaination as to what R^x was and I couldnt understand why it was false.
     
    Last edited: Jul 16, 2007
  2. jcsd
  3. Jul 17, 2007 #2

    matt grime

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    R^[symbol that looks like a multiplication sign] is indeed the multiplicative reals.

    I don't under stand what you're asking. Are you asserting that you know this statement that you imply to be true is actually false? (It is false, by the way, and trivially so - it cannot be that a+b=ab for all a,b in R^x, or for all a,b in a non-trivial subgroup of R^x: any homomorphism of this kind must send 0 to 1.)
     
  4. Jul 17, 2007 #3
    Thanks Matt, I was unsure as to what R^x was and how it worked.
     
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