# does adding any number to any number give an irrational

Watch
Thread starter 10 months ago
#1
hey everyone, so does it if not what numbers add with irrational to give irrational

sorry there is a mistake with the title its suppose to say when any numbers adds with irrational
Last edited by Stormragexox; 10 months ago
0
10 months ago
#2
(Original post by Stormragexox)
hey everyone, so does it if not what numbers add with irrational to give irrational
Any ideas?
What seems to work or not work?
0
Thread starter 10 months ago
#3
(Original post by mqb2766)
Any ideas?
What seems to work or not work?
i tried adding a couple of values with pi and so far i got irrational numbers but i don't know if it would work for all values
0
10 months ago
#4
Try it out with numbers like and

Can you think of any numbers similar to these that would produce just a rational number?
0
10 months ago
#5
(Original post by Stormragexox)
hey everyone, so does it if not what numbers add with irrational to give irrational

sorry there is a mistake with the title its suppose to say when any numbers adds with irrational
I don't fully understand what you're asking.. Im going to assume its:
"does adding any rational number with an irrational number make an irrational number. "
In which the answer is yes. The number created will always be irrational.
0
10 months ago
#6
Can you post the full question

What is
rational + irrational
and why?

Think about counterexamples, does
irrational + irrational
always produce irrational?

(Original post by Stormragexox)
i tried adding a couple of values with pi and so far i got irrational numbers but i don't know if it would work for all values
Last edited by mqb2766; 10 months ago
0
Thread starter 10 months ago
#7
(Original post by mqb2766)
Can you post the full question

What is
rational + irrational
and why?

Think about counterexamples, does
irrational + irrational
always produce irrational?
thx for replying there is not really a direct question from a paper on this, its just a doubt that i had when i had a look at the marking scheme
(Original post by Relentas)
I don't fully understand what you're asking.. Im going to assume its:
"does adding any rational number with an irrational number make an irrational number. "
In which the answer is yes. The number created will always be irrational.

0
10 months ago
#8
Sounds like you know the answer, so maybe include this in the original post?

Can you show
* rational = rational + rational
* irrational = rational + irrational
* ? = irrational + irrational
The proofs shouldn't be more than a few lines ... If not, what do you get stuck on?

(Original post by Stormragexox)
thx for replying there is not really a direct question from a paper on this, its just a doubt that i had when i had a look at the marking scheme

0
Thread starter 10 months ago
#9
(Original post by mqb2766)
Sounds like you know the answer, so maybe include this in the original post?

Can you show
* rational = rational + rational
* irrational = rational + irrational
* ? = irrational + irrational
The proofs shouldn't be more than a few lines ... If not, what do you get stuck on?
yh sorry i didn't adress my problem clearly enough because i was overthinking when i saw the markingscheme
Thx i tried proofing it I understand it now
1
10 months ago
#10
There are a few ways to prove them and its a good question.
Roughly how did you do them?

(Original post by Stormragexox)
yh sorry i didn't adress my problem clearly enough because i was overthinking when i saw the markingscheme
Thx i tried proofing it I understand it now
0
Thread starter 10 months ago
#11
(Original post by mqb2766)
There are a few ways to prove them and its a good question.
Roughly how did you do them?
I don't know if this method is accurate but i used proof by contradiction, regarding the fact i have came across a similar question but in a proof by contradiction style asking to proof rational number - irrational number gives an irrational number, so i tried experimenting this with rational + irrational to proof it would not give an irrational
0
10 months ago
#12
Off the top of my head (and very loosely), for
1) rational + rational, I'd do a/b + c/d which is fairly obviously rational again
2) Assume rational = rational + irrational so irrational = rational - rational. This contradicts 1).
3) (Counter) Examples (as your model solution shows) for rational or irrational = irrational + irrational

(Original post by Stormragexox)
I don't know if this method is accurate but i used proof by contradiction, regarding the fact i have came across a similar question but in a proof by contradiction style asking to proof rational number - irrational number gives an irrational number, so i tried experimenting this with rational + irrational to proof it would not give an irrational
1
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

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

### Poll

Join the discussion

Yes (112)
28.07%
No (287)
71.93%