This is exactly how the book states it.
Let q ∈ Q and a ∈ R\Q
Does a mean real number? I don't even know what R\Q is..
qa is rational if and only if q=0
$\displaystyle \mathbb{R} \backslash \mathbb{Q}$ is the reals with the rationals removed.
So $\displaystyle x \in \mathbb{R} \backslash \mathbb{Q}$ if and only if $\displaystyle x \in \mathbb{R}$ and $\displaystyle x \not\in \mathbb{Q}$.
With that the rest should be easy enough.
CB
yah not really, i figured it was the irrationals, but not sure about proving that heh
the way my teacher does it is he proves both ways.
so in -<<<
Suppose q = 0 = x/y
qa = 0a = 0 =x/y
therefore qa is rational if q=0
but going ->>>>
suppose qa is rational
q=
.
.
.
.
.
=0
that's what i dont understand how to do, i think i understand the first part, but not the second direction.