- #1

missavvy

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## Homework Statement

Using the density of Q(rationals) in R(real numbers), prove the Archimedean property.

## Homework Equations

Density of Q in R: For all x,y in R, and x<y, there exists q in Q s/t x<q<y.

Archimedean property says: For every real number x there exists a natural number y such that y>x.

## The Attempt at a Solution

So I know how to prove the density of Q in R using the Archimedean property but I'm not sure of how to do it the other way around. Also, I don't really understand why it makes sense to prove it the other way around? Any hints and explanations would be helpful! thanks