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# Real numbers

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1. Prove that there is a rational number in the open interval where .
2. http://homepages.warwick.ac.uk/~masdbl/w5.pdf

Look at Assignment 1. See if that helps you.
3. (Original post by Ano123)
Prove that there is a rational number in the open interval where .
is rational and within the range for any thus statement is true. Not sure how to formally structure this sort of proof.
4. (Original post by RDKGames)
is rational and within the range for any thus statement is true. Not sure how to formally structure this sort of proof.
Let and

is not rational.
5. (Original post by Math12345)
Let and

(a+b)/2 is not rational.
oh lol missed that where they don't say a and b are rationals, would be easy otherwise.
6. What have you tried?
7. If , then , if we multiply by some real constant so that ( ) then we can say for sure that some integer lies in that interval which is of course rational. So from this we can deduce that , dividing by we get .
If then an integer lies between the a and b which is obviously rational. This completes the proof.

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