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
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
that's what i dont understand how to do, i think i understand the first part, but not the second direction.