# 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)