You are Here: Home >< Maths

# Real numbers Watch

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.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 6, 2016
Today on TSR

### Anxious about my Oxford offer

What should I do?

### US couple arrested - 13 children chained up

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE