if u>0 is any real number and x<y show there exist a rational number r such that x<ru<y. Hence {ru: r[itex]\in[/itex]Q is dense in R.(adsbygoogle = window.adsbygoogle || []).push({});

I am not sure how to show that there exist a rational number. I was thinking this has something to do with the archimedian property. This is what I have tried

x<[itex]\frac{(x+y)}{2}[/itex]<y

Define r= [itex]\frac{(x+y)}{2}[/itex](1/n) when u>=1 and

r=[itex]\frac{(x+y)}{2}[/itex](n) when u<1

where n is an element of the naturals

but I dont think that works? Any suggestions?

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# Homework Help: Showing Density in R

Can you offer guidance or do you also need help?

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