It's been so long since I took discrete math, maybe someone here can help me with what ought to be a straight forward and simple proof.
Effectively I want to show this:
- Let a and b be positive integers where b>a and b != 0. (a/b is a rational number between 0 and 1, non-inclusive).
- Let k and l be (real?) numbers where k = l(a/b)
- (Meat of the proof here)
- Then for any l, k < l.
My discrete book doesn't really get into quite this case, and I don't really know what to search for here to find this type of proof. Thanks!
First of all you need $l>0$ to have the result.
$$l-k=l-l\frac{a}b=l\frac{b-a}b>0$$ as $l$ and $\frac{b-a}b$ are both positive. So, $l>k$.