If a<b should that..

**Barthayn** · September 30th 2011, 06:26 PM

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?

**FernandoRevilla** · September 30th 2011, 07:51 PM

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 $\mathbb{R}-\{0\}$ then, $a<b$ iff $b-a>0$ . Then, $\frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}>0$ iff $a$ and and $b$ have the same sign.

Thread: If a<b should that..

LinkBack

Thread Tools

Display

If a<b should that..

Re: If a<b should that..

Search Tags