ok.. I have a function f such that f(x + y) = f(x) + f(y)
I have proves f(nx) = nf(x) for all x and every natural number n
I now need to show that this is true for f(rx) where f is a rational number n/m
I've tried fixing m and doing induction on n but I cant do it by fixing n and doing induction on m, is this the right way of going about it?
many thanks