1
$\begingroup$

Let a function exist such that $f(a+b)=f(a)+f(b)$. We have already shown that for any integer n, $f(nx)=n f(x)$. Now we must show that for any rational number $n/m$, $f(n/m)=n/m f(1)$.

The problem is that showing the equation for integers was easy, as multiplication is repeated addition. However, the same can't be done for division.

  • 0
    Hint: $m f(n/m)=?$2012-12-13

1 Answers 1