# irrational between any two rational proof

• Mar 14th 2008, 08:11 PM
60beetle
irrational between any two rational proof
Hey guys new to the forum and have a question of my own,

I need to prove that for x and y where x<y and both x and y are rational, there exists z where x<z<y and z is irrational.

the previous part of the question was to find the smallest positive integer n such that ((2)^1/2)/n < .00001

I think I'm supposed to use this and contradiction to prove one exists as contradiction was used in proofs in the question before

any help will be greatly apprecitated
• Mar 15th 2008, 02:04 AM
Opalg
Quote:

Originally Posted by 60beetle
I need to prove that for x and y where x<y and both x and y are rational, there exists z where x<z<y and z is irrational.

My suggestion: $z = x + (y-x)/\sqrt2$.
• Mar 15th 2008, 09:45 PM
60beetle
Quote:

Originally Posted by Opalg
My suggestion: $z = x + (y-x)/\sqrt2$.

Thanks for that, I knew it would be something relativly simple but it was just one of those days I couldn't get my head around the problem