(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that f:R->Q (reals to rationals) is a ring homomorphism. Prove that f(x)=0 for every x in the reals.

2. Relevant equations

Homomorphisms map the zero element to the zero element.

f(0) = 0

Homomorphisms preserve additive inverses.

f(-a)=-f(a)

and finally,

f(a - b) = f(a) - f(b)

3. The attempt at a solution

My guess is go with contradiction and say, Suppose that f(a != 0) != 0 for some a in the reals.

But I don't see where to go from there. A hint or suggestion would be nice.

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# Homework Help: Property of a ring homomorphism

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