as per me the above statement have to be true because if the sum of two irrational number is 0 , it suggests that 2 irrational numbers have to be prefer +k and also -k whereby k is an irrational number . Additionally when diffrence of 2 irrational numbers is rational it is possible only once both the irrational number are very same . Indigenous both the above cases we have the right to conclude that if amount of 2 irrational number is rational or difference of 2 irrational numbers is rational then it must be 0 . You re welcome correct me if ns am dorn . By "a" and also "b" i mean solitary or separation, personal, instance irrational numbers for instance only "pi" and also not "pi +/- something" .

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edited jan 18 "20 at 7:28
Sameer nilkhan
asked jan 18 "20 in ~ 6:16
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Sameer nilkhanSameer nilkhan
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If $a+b$ and also $a-b$ are both rational, climate so is $a$ since it is the median of those two quantities, and the average of two rational numbers is likewise rational. Thus additionally $b=(a+b)-a$ is rational.


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answered january 18 "20 in ~ 6:21
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pre-kidneypre-kidney
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Your statement in the body is not correct. For example, both $sqrt 2$ and also $sqrt 2 +1$ are irrational. Their distinction is $1$, i m sorry is rational. If both the sum and difference of two numbers space rational, the 2 numbers need to be rational, but that is not what your question says.


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answered jan 18 "20 in ~ 6:26
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Ross MillikanRoss Millikan
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Don"t overthink it.

If $x$ irrational climate $q - x$ is irrational for every reasonable $q$.

So $x + (q-x) = q$ is the rational sum of two irrational numbers. But $q$ can be any type of rational number and doesn"t have to be $0$.

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This is just one of those results that when you analyze it you establish it can"t actually mean anything.

We think. $rational + reasonable = rational$

And $rational + irrational = irrational$.

But what the $irrational + irrational$ can that be rational.

Well, $sqrt 2 + (-sqrt 2) = 0$ and $0$ is reasonable so it deserve to be rational.

So us think... And we say... Yeah, however $sqrt 2$ and $-sqrt 2$ are pertained to each other, they room negatives of each other. Ns bet if you have two independent irrationals the must include to a irrational.

So who else states well if $x +y = k$ and also $k$ is rational, climate if $x$ is irrational climate $y= k - x$ is irrational and $x + y = x+(k-x) = k$. So the is 2 irrationals that include to a rational.

So we say... Yet those are dependent to every other; i bet if you have two independent irrationals the must include to a irrational.

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So the other person asks. How exactly to you define if two irrationals are "dependent"?

And us say... Fine if $x$ is irrational and $y = pm x + k$ for part rational $k$ they space dependent. Therefore I case that if $x,y$ room independent 보다 $x + y$ is no rational.

And climate other person says.... For this reason in various other words, you space claiming that there is no reasonable number $k$ so that $y =pm x + k$ then $y mp x e k$ for any rational $k$ however if over there is such a rational $k$ so the $y =pm x + k$ then $ymp x$ might be rational; is the what you are claiming?

And us say, yes, currently how have the right to I prove it?

And the other person says. Um... You just said $x mp y =k; k$ reasonable if and also only if $x = pm y +k$ for some rational $k$. Carry out you really think that is meaningful?