1. ## rational numbers proof

Let $\displaystyle a,b \epsilon R,$ with $\displaystyle a<b$. Show that there exists a number $\displaystyle x\epsilon R$ such that $\displaystyle a<x<b,$ with $\displaystyle x$ rational or not rational, as we wish.

Thank you!!!!

2. Originally Posted by Barton
Let $\displaystyle a,b \epsilon R,$ with $\displaystyle a<b$. Show that there exists a number $\displaystyle x\epsilon R$ such that $\displaystyle a<x<b,$ with $\displaystyle x$ rational or not rational, as we wish.

Thank you!!!!
Choose
$\displaystyle x = \frac{a + b}{2}$

I leave it to you to show that x has the required property.

-Dan