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# An Interesting Question

what is the answer of the question? (100-100)/(10-10)

Note by Manish Agarwal
4 years, 8 months ago

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Not exactly "undefined"; a more fitting term would be "indeterminate", because any number $$x$$ multiplied by zero is zero.

- 4 years, 8 months ago

How to make crazy work: Say $$x$$ is a number arbitrarily close to $$10$$ but not exactly $$10$$. We need to find $$\lim_{x\to 10} \frac{x^2-100}{x-10}=\lim_{x\to 10} x+10=20$$

- 4 years, 8 months ago

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

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

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.

Staff - 4 years, 8 months ago

as from what i learned the real and specific term for 0/0 is INDETERMINATE not undefined

- 4 years, 8 months ago

UNDEFINED

- 4 years, 8 months ago

i wish mathematics had something better to offer :/

- 4 years, 8 months ago

Comment deleted Feb 18, 2013

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

- 4 years, 8 months ago

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

- 4 years, 8 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..??

- 4 years, 8 months ago

why is sayan C spamming :\

- 4 years, 8 months ago

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

- 4 years, 8 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.

- 4 years, 8 months ago

would u please state your ' a few theorem'...i do not know it...

- 4 years, 8 months ago

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

- 4 years, 8 months ago

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

- 4 years, 8 months ago

u can not divide anything by zero.

- 4 years, 8 months ago

Though on the *crazy side* {If that was what u meant by "interesting", $$(100-100)/(10-10)$$ = $$10(10-10)/(10-10)$$ = $$10$$ }

- 4 years, 8 months ago

no cancellation rule applies for zero

- 4 years, 8 months ago

Yes, I know..why isn't anyone noticing *"crazy side"* in my comment??

- 4 years, 8 months ago

I do. :)

- 4 years, 8 months ago

Thanks man! :)

- 4 years, 8 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...

- 4 years, 8 months ago

Dude..chill! that was why i told "On the *crazy* side"

- 4 years, 8 months ago

1. XD

- 4 years, 8 months ago

cant be determined

- 4 years, 8 months ago

indeterminate

- 4 years, 8 months ago

It is Undetermined or Undefined.

- 4 years, 8 months ago

and UNDEFINED tooo

- 4 years, 8 months ago

(100-100)/(10-10) is nothing but indeterminate form ....which cannot be solved...we may solve it using limits

- 4 years, 8 months ago

0/0

- 4 years, 8 months ago

UNDEFINED

- 4 years, 8 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

- 4 years, 8 months ago

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

- 4 years, 8 months ago

it can be (10^{2}-10^{2})/(10-10) =(10+10)(10-10)/(10-10) =20

- 4 years, 8 months ago

how can you cancel zero by zero?????

- 4 years, 8 months ago

i agree with that point

- 4 years, 8 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.

- 4 years, 8 months ago

It can be 20 :

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

- 4 years, 8 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 wrong

- 4 years, 8 months ago

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 ^^

- 4 years, 8 months ago

use limit bro

- 4 years, 8 months ago

0

- 4 years, 8 months ago

10(10-10)/(10-10) = 10

- 4 years, 8 months ago