# Thread: If a<b should that..

1. ## If a<b should that..

If a<b should that 1/a > 1/b. I know that this is true, and I know that I can prove this by assuming a and b are natural numbers, but is there any other way of proving this statement?

2. ## Re: If a<b should that..

Originally Posted by Barthayn
If a<b should that 1/a > 1/b. I know that this is true, and I know that I can prove this by assuming a and b are natural numbers, but is there any other way of proving this statement?
If you mean to prove it in $\displaystyle \mathbb{R}-\{0\}$ then, $\displaystyle a<b$ iff $\displaystyle b-a>0$ . Then, $\displaystyle \frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}>0$ iff $\displaystyle a$ and and $\displaystyle b$ have the same sign.