Proof the following using denseness in reals

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February 28th 2008, 07:05 AM
sthato

Proof the following using denseness in reals

if x in an rational number but not equal to zero and y is an irrational number. Proof that x/y is an irrational number?
February 28th 2008, 08:24 AM
JaneBennet

If $\frac{x}{y}$ is rational, then $y=x\left(\frac{x}{y}\right)^{-1}$ is rational too. ( $\left(\frac{x}{y}\right)^{-1}$ exists as $x\ne0$ .) Contrapositively, if $y$ is irrational, $\frac{x}{y}$ must be irrational.
February 28th 2008, 09:44 AM
sthato

Thanks

Thanks for your help Jane.(Yes)

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