rational numbers proof

**Barton** · September 9th 2008, 09:30 AM

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

Thank you!!!!

**topsquark** · September 9th 2008, 10:13 AM

Originally Posted by Barton

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

Thank you!!!!

Choose
$x = \frac{a + b}{2}$

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

-Dan

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