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Math Help - If a<b should that..

  1. #1
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    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?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: If a<b should that..

    Quote Originally Posted by Barthayn View Post
    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.
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