Not exactly "undefined"; a more fitting term would be "indeterminate", because any number \(x\) multiplied by zero is zero.
–
Francis Gerard Magtibay
·
3 years, 11 months ago

Log in to reply

How to make crazy work:
Say \(x\) is a number arbitrarily close to \(10\) but not exactly \(10\). We need to find \(\lim_{x\to 10} \frac{x^2-100}{x-10}=\lim_{x\to 10} x+10=20\)
–
Abhishek De
·
3 years, 11 months ago

Log in to reply

@Abhishek De
–
The main problem with this is that your expression is 'completely arbitrary'. For example, I could say that

Adapting this idea, you could arrive at any numerical answer you want. Hence, limits would be unable to resolve this issue, as it is highly dependent on the path that you arrive at the limit.

Note: A similar problem is to define \(0^0\) though limits. "Most of the time" we get 1, though if you take \( \lim_{x \rightarrow 0} 0^x\), you will get 0.
–
Calvin Lin
Staff
·
3 years, 11 months ago

Log in to reply

as from what i learned the real and specific term for 0/0 is INDETERMINATE not undefined
–
Arlo Andallo
·
3 years, 11 months ago

@Sridhar Thiagarajan
–
Don't u know when we write (x^2-y^2)/(x-y)=(x+y) ,it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =(x+y) as result,..here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrong
–
Sayan Chowdhury
·
3 years, 11 months ago

@Kevin Lloyd Esguerra
–
but u see there is no "limit' given as x-->10 while i can perform it as a limit problem ,... isn't it..??
–
Sayan Chaudhuri
·
3 years, 11 months ago

Log in to reply

why is sayan C spamming :\
–
Soham Chanda
·
3 years, 11 months ago

Log in to reply

answer is 20!
may sound crazy. But as I go thru discussions, the fact x + y could be the answer is presented.

whenever you encounter 'zero upon zero' situation, it is of course 'indeterminate' - but it also means that is not the end. There is a real answer different from 'indeterminate'. You may arrive at it by suitable algebraic simplification / trigonometry simplification etc.

There are even a few theorems to work out the real answers
–
Raghunathan N.
·
3 years, 11 months ago

Log in to reply

@Raghunathan N.
–
The question is not (x^2-100)/(x-10) with x tending to zero. We can interpret (100-100)/(10-10) in different ways and get different answers as Calvin said. So the answer does not necessarily have to be 20.
For eg. the question can be interpreted as lim x->10 [(x^3-9x^2-100)/(x-10)] which gives the answer as 120. So I think answer is undefined.
–
Ashwin Venkatraman
·
3 years, 11 months ago

@Sayan Chaudhuri
–
remember ....it is the problem only (100-100)/(10-10)=?...& not anything should be thought or taken into account....
–
Sayan Chaudhuri
·
3 years, 11 months ago

Log in to reply

many possible answers are there.....like 10,20,undefuned,etc... depending on the person who solve it...
–
Pradeep Ravichandran
·
3 years, 11 months ago

Log in to reply

u can not divide anything by zero.
–
Nishanth Hegde
·
3 years, 11 months ago

Log in to reply

@Nishanth Hegde
–
Though on the *crazy side* {If that was what u meant by "interesting",
\((100-100)/(10-10)\) = \(10(10-10)/(10-10)\) = \(10\) }
–
Nishanth Hegde
·
3 years, 11 months ago

@Nishanth Hegde
–
Don't u know when we write [a(x-y)/(x-y)=a] it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =a as result...here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrong...
–
Sayan Chowdhury
·
3 years, 11 months ago

(100-100)/(10-10) is nothing but indeterminate form ....which cannot be solved...we may solve it using limits
–
Harshit Khandelwal
·
3 years, 11 months ago

Undefined. The division of 0 is not allowed in Maths since you can get a variety of answers. Since anything mutiplied by 0 is 0, 0 divided by 0 is everything. Like wise, nothing multiplied by 0 is not 0, hence any other number divided by 0 is just not possible
–
Hongyi Shen
·
3 years, 11 months ago

Log in to reply

Hey you can't divide by zero ..... there are plethora of mathematical contradictions and absurdities based on division by zero ....... If you divide by zero serious flaws creep into your logic leading to absolute fallacies
–
Jaydutt Kulkarni
·
3 years, 11 months ago

Log in to reply

it can be (10^{2}-10^{2})/(10-10)
=(10+10)(10-10)/(10-10)
=20
–
Manish Agarwal
·
3 years, 11 months ago

@Manish Agarwal
–
We can only cancel the term taking the supposition that it is not zero. So, if you want to cancel a term you will have to assume that it is not zero. So, in this case you cannot cancel the term my friend. so, your answer is totally wrong.
–
Brilliant Kumar
·
3 years, 11 months ago

many possible answers are there.....like 10,20,undefined,etc... depending on the person who solve it...

https://brilliant.org/discussions/thread/an-interesting-question/#comment-a3f52161e92
–
Zi Song Yeoh
·
3 years, 11 months ago

Log in to reply

@Manish Agarwal
–
Don't u know when we write (x^2-y^2)/(x-y)=(x+y) ,it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =(x+y) as result,..here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrong
–
Sayan Chowdhury
·
3 years, 11 months ago

Log in to reply

hi
it's not possible, you cannot divide any real by 0, so dividing 0 by it's self is one of the craziest thing I saw, since a/0 might me greater than infinit, because that infinit times 0 is still 0, but I cannot guess what might be 0/0, since it could be \(0^{23-5}=0\) , \(0^{1-23}=1/0\) or even \(0^{0}\) or 0^ any number ,we can accept the strictly positive ones, but not the the others , so this is particularly weird I think

but I guess you know all this stuff already ^^
–
Anas Elidrissi
·
3 years, 11 months ago

## Comments

Sort by:

TopNewestNot exactly "undefined"; a more fitting term would be "indeterminate", because any number \(x\) multiplied by zero is zero. – Francis Gerard Magtibay · 3 years, 11 months ago

Log in to reply

How to makeSay \(x\) is a number arbitrarily close to \(10\) but not exactly \(10\). We need to find \(\lim_{x\to 10} \frac{x^2-100}{x-10}=\lim_{x\to 10} x+10=20\) – Abhishek De · 3 years, 11 months agocrazywork:Log in to reply

\[ \lim_{x \rightarrow 10} \frac { \frac {1}{2} x^2 + 5x - 100}{ x-10} = \lim_{x \rightarrow 10} \frac {1}{2} x + 10 = 15.\]

Adapting this idea, you could arrive at any numerical answer you want. Hence, limits would be unable to resolve this issue, as it is highly dependent on the path that you arrive at the limit.

Note: A similar problem is to define \(0^0\) though limits. "Most of the time" we get 1, though if you take \( \lim_{x \rightarrow 0} 0^x\), you will get 0. – Calvin Lin Staff · 3 years, 11 months ago

Log in to reply

as from what i learned the real and specific term for 0/0 is INDETERMINATE not undefined – Arlo Andallo · 3 years, 11 months ago

Log in to reply

UNDEFINED – Shourya Pandey · 3 years, 11 months ago

Log in to reply

– Harshit Kapur · 3 years, 11 months ago

i wish mathematics had something better to offer :/Log in to reply

Log in to reply

– Sayan Chowdhury · 3 years, 11 months ago

Don't u know when we write (x^2-y^2)/(x-y)=(x+y) ,it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =(x+y) as result,..here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrongLog in to reply

– Kevin Lloyd Esguerra · 3 years, 11 months ago

there is nothing wrong with the solution. study about "limits" bro, it helps sometimes.Log in to reply

– Sayan Chaudhuri · 3 years, 11 months ago

but u see there is no "limit' given as x-->10 while i can perform it as a limit problem ,... isn't it..??Log in to reply

why is sayan C spamming :\ – Soham Chanda · 3 years, 11 months ago

Log in to reply

answer is 20! may sound crazy. But as I go thru discussions, the fact x + y could be the answer is presented.

whenever you encounter 'zero upon zero' situation, it is of course 'indeterminate' - but it also means that is not the end. There is a real answer different from 'indeterminate'. You may arrive at it by suitable algebraic simplification / trigonometry simplification etc.

There are even a few theorems to work out the real answers – Raghunathan N. · 3 years, 11 months ago

Log in to reply

– Ashwin Venkatraman · 3 years, 11 months ago

The question is not (x^2-100)/(x-10) with x tending to zero. We can interpret (100-100)/(10-10) in different ways and get different answers as Calvin said. So the answer does not necessarily have to be 20. For eg. the question can be interpreted as lim x->10 [(x^3-9x^2-100)/(x-10)] which gives the answer as 120. So I think answer is undefined.Log in to reply

– Sayan Chaudhuri · 3 years, 11 months ago

would u please state your ' a few theorem'...i do not know it...Log in to reply

– Sayan Chaudhuri · 3 years, 11 months ago

remember ....it is the problem only (100-100)/(10-10)=?...& not anything should be thought or taken into account....Log in to reply

many possible answers are there.....like 10,20,undefuned,etc... depending on the person who solve it... – Pradeep Ravichandran · 3 years, 11 months ago

Log in to reply

u can not divide anything by zero. – Nishanth Hegde · 3 years, 11 months ago

Log in to reply

{If that was what u meant by "interesting", \((100-100)/(10-10)\) = \(10(10-10)/(10-10)\) = \(10\) } – Nishanth Hegde · 3 years, 11 months ago*crazy side*Log in to reply

– Akbarali Surani · 3 years, 11 months ago

no cancellation rule applies for zeroLog in to reply

in my comment?? – Nishanth Hegde · 3 years, 11 months ago*"crazy side"*Log in to reply

– Zi Song Yeoh · 3 years, 11 months ago

I do. :)Log in to reply

– Nishanth Hegde · 3 years, 11 months ago

Thanks man! :)Log in to reply

– Sayan Chowdhury · 3 years, 11 months ago

Don't u know when we write [a(x-y)/(x-y)=a] it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =a as result...here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrong...Log in to reply

side" – Nishanth Hegde · 3 years, 11 months ago*crazy*Log in to reply

Log in to reply

cant be determined – Superman Son · 3 years, 11 months ago

Log in to reply

indeterminate – Sri Krishna Priya Dhulipala · 3 years, 11 months ago

Log in to reply

It is Undetermined or Undefined. – Rukkesh Vinoth · 3 years, 11 months ago

Log in to reply

and UNDEFINED tooo – Yatharth Pandey · 3 years, 11 months ago

Log in to reply

(100-100)/(10-10) is nothing but indeterminate form ....which cannot be solved...we may solve it using limits – Harshit Khandelwal · 3 years, 11 months ago

Log in to reply

0/0 – Veeramanoharan Rajamannar · 3 years, 11 months ago

Log in to reply

UNDEFINED – Ayush Maheshwari · 3 years, 11 months ago

Log in to reply

Undefined. The division of 0 is not allowed in Maths since you can get a variety of answers. Since anything mutiplied by 0 is 0, 0 divided by 0 is everything. Like wise, nothing multiplied by 0 is not 0, hence any other number divided by 0 is just not possible – Hongyi Shen · 3 years, 11 months ago

Log in to reply

Hey you can't divide by zero ..... there are plethora of mathematical contradictions and absurdities based on division by zero ....... If you divide by zero serious flaws creep into your logic leading to absolute fallacies – Jaydutt Kulkarni · 3 years, 11 months ago

Log in to reply

it can be (10^{2}-10^{2})/(10-10) =(10+10)(10-10)/(10-10) =20 – Manish Agarwal · 3 years, 11 months ago

Log in to reply

– Namra Aziz · 3 years, 11 months ago

how can you cancel zero by zero?????Log in to reply

– Sayan Chaudhuri · 3 years, 11 months ago

i agree with that pointLog in to reply

– Brilliant Kumar · 3 years, 11 months ago

We can only cancel the term taking the supposition that it is not zero. So, if you want to cancel a term you will have to assume that it is not zero. So, in this case you cannot cancel the term my friend. so, your answer is totally wrong.Log in to reply

be 20 :canhttps://brilliant.org/discussions/thread/an-interesting-question/#comment-a3f52161e92 – Zi Song Yeoh · 3 years, 11 months ago

Log in to reply

– Sayan Chowdhury · 3 years, 11 months ago

Don't u know when we write (x^2-y^2)/(x-y)=(x+y) ,it is given or we assume that, x is not equal to y...or (x-y)is not equal to zero....and only then we divide both the numerator and denominator by (x-y)...and we get =(x+y) as result,..here we are seeing clearly (10-10)=0 so we cannot proceed with such a operation...and the result we would get be absolute wrongLog in to reply

hi it's not possible, you cannot divide any real by 0, so dividing 0 by it's self is one of the craziest thing I saw, since a/0 might me greater than infinit, because that infinit times 0 is still 0, but I cannot guess what might be 0/0, since it could be \(0^{23-5}=0\) , \(0^{1-23}=1/0\) or even \(0^{0}\) or 0^ any number ,we can accept the strictly positive ones, but not the the others , so this is particularly weird I think

but I guess you know all this stuff already ^^ – Anas Elidrissi · 3 years, 11 months ago

Log in to reply

use limit bro – Ahmad Widardi · 3 years, 11 months ago

Log in to reply

0 – Yatharth Pandey · 3 years, 11 months ago

Log in to reply

10(10-10)/(10-10) = 10 – Kim Joshua Desposado · 3 years, 11 months ago

Log in to reply