(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let x and y be real numbers with x<y and write an inequality involving a rational

number p/q capturing what we need to prove. Multiply everything in your inequality by q,

then explain why this means you want q to be large enough so that q(y-x)>1 . Explain

how you can rewrite this inequality and use the Archimedean property to find such a q.

3. The attempt at a solution

So, this is a question on a worksheet our teacher gave us to go along with the theorem in the book. Here is what I did so far:

x < p/q < y

Then multiply both sides by q as the question states:

qx < p < yq

0 < p-qx < yq-qx

0 < p-qx < q(y-x)

I am having trouble seeing why q(y-x)>1. It is obviously great than zero as the inequality states, but can someone help me see why it has to be >1??

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# Homework Help: Between any two distinct real numbers there is a rational number

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