You are Here: Home >< Maths

# Prove that the sum, difference and the product of two integers is also an integer.

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
1. So I have an idea of how to do this, but it seems a bit two tedious and im sure there is a more elegant way. I'm looking at question 9 below:

My idea would be to look at different cases. Like we start by letting a and b be integers. Then we look at the different cases depending on the signs of a and b.

Problem is with the fact that they need to use the previous exercise, which is also in the picture above.

Any ideas?
2. I think continuing with induction would be the way to go. Results likes these seem so trivial, that it sometimes makes proving it seem harder than proving more difficult results.
3. (Original post by B_9710)
I think continuing with induction would be the way to go. Results likes these seem so trivial, that it sometimes makes proving it seem harder than proving more difficult results.
Yeh but you would have to do induction up and down for all integers.

Posted from TSR Mobile
4. (Original post by gagafacea1)
So I have an idea of how to do this, but it seems a bit two tedious and im sure there is a more elegant way. I'm looking at question 9 below:

My idea would be to look at different cases. Like we start by letting a and b be integers. Then we look at the different cases depending on the signs of a and b.

Problem is with the fact that they need to use the previous exercise, which is also in the picture above.

Any ideas?
Prove that n+m n,mEN is a nat number.
Then without induction on integers.
Fact is that, if you have a difference of integers or sum it is either a natual number or
-(natural number) so proving the sum or difference is essentially the same thing wlog. That is if you can assum that if a is an integer then -a is an integer. If you canmt assume that, i can't be bothered to try anything else

Posted from TSR Mobile
5. (Original post by B_9710)
I think continuing with induction would be the way to go. Results likes these seem so trivial, that it sometimes makes proving it seem harder than proving more difficult results.
(Original post by physicsmaths)
Prove that n+m n,mEN is a nat number.
Then without induction on integers.
Fact is that, if you have a difference of integers or sum it is either a natual number or
-(natural number) so proving the sum or difference is essentially the same thing wlog. That is if you can assum that if a is an integer then -a is an integer. If you canmt assume that, i can't be bothered to try anything else

Posted from TSR Mobile
To be honest I still don't see how I could do that. I guess my biggest problem is that I don't know what I can assume to be defined and what I can't. Like how deep should I go with the proof? I've done all of the problems below except for the last:

This is how integers are defined in the book:
Attachment 558217558219
Attached Images

6. What module is this?
7. (Original post by Chittesh14)
What module is this?
It's not an A-Level module.
8. (Original post by Zacken)
It's not an A-Level module.
No... as in what module does this content come under?
9. (Original post by Chittesh14)
No... as in what module does this content come under?
Number Theory, it's a course - not a module.
10. (Original post by Zacken)
Number Theory, it's a course - not a module.
Oh lmao.....

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: July 1, 2016
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:
Today on TSR

### Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams