# does adding any number to any number give an irrational

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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__
Last edited by Stormragexox; 2 years ago

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#2

(Original post by

hey everyone, so does it if not what numbers add with irrational to give irrational

**Stormragexox**)hey everyone, so does it if not what numbers add with irrational to give irrational

What seems to work or not work?

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#4

Try it out with numbers like and

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

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

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#5

Can you post the full question

What is

rational + irrational

and why?

Think about counterexamples, does

irrational + irrational

always produce irrational?

What is

rational + irrational

and why?

Think about counterexamples, does

irrational + irrational

always produce irrational?

(Original post by

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

**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; 2 years ago

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(Original post by

Can you post the full question

What is

rational + irrational

and why?

Think about counterexamples, does

irrational + irrational

always produce irrational?

**mqb2766**)Can you post the full question

What is

rational + irrational

and why?

Think about counterexamples, does

irrational + irrational

always produce irrational?

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#7

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?

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

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

**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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(Original post by

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?

**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?

Thx i tried proofing it I understand it now

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#9

There are a few ways to prove them and its a good question.

Roughly how did you do them?

Roughly how did you do them?

(Original post by

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

**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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(Original post by

There are a few ways to prove them and its a good question.

Roughly how did you do them?

**mqb2766**)There are a few ways to prove them and its a good question.

Roughly how did you do them?

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#11

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

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

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

**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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