Reals under multiplication homomorphisms

[ldelong]

Homework Statement

A function f:R-->R^x is a homomorphism iff f(x+y) = f(x) + f(y) for all x,y in R

Homework Equations

I don't 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?

The Attempt at a Solution

This isn't a homework question, I read it in the book as a false statement but there was no explanation as to what R^x was and I couldn't understand why it was false.

 

[matt grime]

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.)

 

[ldelong]

Thanks Matt, I was unsure as to what R^x was and how it worked.