Proof by contradictionTheorem: The reciprocal of any irrational number is irrational.

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- May 6th 2013, 09:14 AMzhengcl86Proof by Contradiction help, no clue, lost
Proof by contradictionTheorem: The reciprocal of any irrational number is irrational.

- May 6th 2013, 09:35 AMPlatoRe: Proof by Contradiction help, no clue, lost
- May 6th 2013, 09:44 AMmathguy25Re: Proof by Contradiction help, no clue, lost
Lemma: If is rational, then is rational.

Proof: Let be rational. Then where are integers with and . Then . Thus, and since we see that . Thus, is rational.

Now let be irrational and assume by contradiction that is rational. Then by the Lemma, is rational. But, which means a rational number equals an irrational number, a contradiction. Thus, is irrational.