does adding any number to any number give an irrational

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Stormragexox
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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
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mqb2766
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(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?
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Stormragexox
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(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
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Lemur14
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Try it out with numbers like 2+\sqrt{2} and 4-\sqrt{3}

Can you think of any numbers similar to these that would produce just a rational number?
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mqb2766
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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
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Stormragexox
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(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

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mqb2766
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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

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Stormragexox
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(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
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mqb2766
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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
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Stormragexox
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(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
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mqb2766
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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
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