# Prove by Archimedian property

• February 28th 2011, 09:23 AM
rainyice
Prove by Archimedian property
Here is the problem:

Use the Archimedian property to prove that if a,b belongs to R (real number) with 0< a < b, then there is a rational number p/q with p and q both odd such that a<p/q<b. (Remark: Modify the proof that rationals are dense.)

Here is my work:

By the Archimedian property, there exists an odd q belongs to R such that 1 < qa implies that 1/q < a. By the Archimedian property agian, there exists an odd p belongs to R such that a<p/q<b.

Is it right???
• February 28th 2011, 09:39 AM
Plato
Can you show that if $c-d>1$ then there is an integer such that $d
If so we know there us an integer such that $1 So $\dfrac{J}{K}$ is between them.
• February 28th 2011, 07:44 PM
rainyice
Thank you ~ problem solved