x=yx=y

x2=xyx^2=xy

x2y2=xyy2x^2 - y^2=xy - y^2

(x+y)(xy)=y(xy)(x + y)(x - y)= y(x - y)

x+y=yx + y=y

1+1=11 + 1=1

What is the fallacy?

Note by Sharky Kesa
6 years, 5 months ago

No vote yet
1 vote

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Comments

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x=yx = y This means xy=0x-y = 0.

In step 44 you have cancelled 00 from both sides!!The world just exploded!!!

Eddie The Head - 6 years ago

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What if it has? What if this is the afterlife?

Sharky Kesa - 6 years ago

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it's good to see this.... see this what your proof says in terms of 11 1=112=1×11212=1×112(1+1)(11)=1(11)andyoucancelled(11)i.e.0frombothsideswhichmeans00thatdoesntexist1=1\\ { 1 }^{ 2 }=1\times 1\\ { 1 }^{ 2 }-{ 1 }^{ 2 }=1\times 1-{ 1 }^{ 2 }\\ (1+1)(1-1)=1(1-1)\\ and\quad you\quad cancelled\quad (1-1)\quad i.e.\quad 0\quad from\quad both\quad sides\\ which\quad means\quad \frac { 0 }{ 0 } \quad that\quad doesn't\quad exist

please give me suggestion if i am wrong

Rishabh Jain - 6 years ago

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How about this?

-20=-20

4²-9x4=5²-9x5

4²-9x4+81/4=5²-9x5+81/4

(4-9/2)²=(5-9/2)²

4-9/2=5-9/2

4=5

2+2=5

Debarpan Adhikari - 6 years ago

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If x^2=y^2, it doesn't necessarily mean that x=y, it means x=+-y as y can be negative also.

Kushagra Sahni - 6 years ago

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But in the first step it is given that x=y which implies that both the variables have to have the same sign,unless they both are zero.

Adarsh Kumar - 6 years ago

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@Adarsh Kumar No, you are wrong!!! What do you think sqrt. 16 is ? Of course, it is 4 but why can't it be -4 ?

Kushagra Sahni - 6 years ago

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@Kushagra Sahni I get that x^2 =y^2 can have two outcomes but what I am trying to tell u is that x and y have the same signs and this can be seen in the 1st step of the falla ie.Get that.

Adarsh Kumar - 6 years ago

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@Adarsh Kumar 16 is just a random example to prove that sqrt. of any real number can be both positive or negative, unless specified otherwise that x>0 or x<0

Kushagra Sahni - 6 years ago

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when you take the square root of both sides, you have to add plus or minus sign, and remove extraneous solutions.

Siva M. - 6 years ago

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since x^1/2 is = +x therefore you can't write 4^2-9*4+81/4 = (4-9/2)^2 it must be written as

(9/2-4)^2=(5-9/2)^2 ie 9/2-4=5-9/2 => 9=9

Aakash Khandelwal - 5 years, 10 months ago

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4-9/2 is obviously a negative number it's equal to -0.5 you should have realized that the square root of a negative number do not exist imaginary only, so you cannot take the square root of the both sides :)

Marchan Sy - 6 years ago

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Really, 2+2=5, I checked it using MS Excel: pic.twitter.com/iS9BNigN3p ;)

Jurii Mariinsky - 5 years, 11 months ago

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I think 4th line has defect.

Abdur Rehman Zahid - 5 years, 6 months ago

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if we taking square root then there are two ans one is positive second one is negetive having magnitude same so we have to assume both cases....

nandkishor wankhede - 6 years ago

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This one's good,

1=1-1=-1

11=11\frac {-1}{1}=\frac {1}{-1}

11=11\sqrt{\frac {-1}{1}}=\sqrt{\frac {1}{-1}}

11=11\frac {\sqrt{-1}}{\sqrt{1}}=\frac {\sqrt{1}}{\sqrt{-1}}

i1=1i\frac {i}{1}=\frac {1}{i}

i2=1i^{2}=1

1=1.-1=1.\quad \square

Ahmad Naufal Hakim - 6 years ago

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Quotient rule for radicals xy=xy\sqrt{\frac{x}{y}}=\frac{\sqrt{x}}{\sqrt{y}} only applies when xx and yy are non-negative, and that y0y \neq 0. So, the third to fourth line of solution is faulty.

Jaydee Lucero - 6 years ago

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You found it. :D

Ahmad Naufal Hakim - 6 years ago

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I completely agree with you

Vijitendra D - 6 years ago

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u have to put both + and - while removing the root sign!!

Gunjas Singh - 6 years ago

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Wrong

Sharky Kesa - 6 years ago

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YES, SAME CONCEPT. IF X^2=Y^2, THEN X IS NOT NECESSARILY = TO Y, IT CAN BE -Y ALSO

Kushagra Sahni - 6 years ago

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If x=y , then x-y = 0 Hence we cannot cancel (x-y) in the 5th step coz a number divided by 0 is not defined in mathematics. So even if you prove that 1+1=1(which is not likely to happen).....it won't be practical in real life

Vijitendra D - 6 years ago

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u r not allowed to cancel 0 from both sides...i mean (x-y)

Abhishek Bakshi - 6 years ago

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Mr. Sharky....you can divide an inequality only by a non zero number....here when you have assumed x=y...then x-y becomes zero....and this is the reason you are getting 2=1

Vikrant Yadav - 6 years ago

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Zero by zero is indeterminate form.. You cannot cancel zero by zero.. (x-y)=0

Steve Stanley - 6 years ago

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in 4th line do---x^2+y^2-2xy=xy-y^2

then solve it as, x^2+2y^2-3xy=0

it forms x^2-3xy+2y^2=0

x^2-xy-2xy+2y^2=0

x(x-y)-2y(x-y)=0

(x-2y)(x-y)=0

x=2y or x=y

hence x=y proved;;;;;;

Yashasvini Sharma - 6 years ago

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A very good one this is but you know the problem with this.

Adarsh Kumar - 6 years ago

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Yes I do.

Sharky Kesa - 6 years ago

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You got x+y=y x + y = y . Doesn't this imply x=0 x = 0 and consequently y=0 y = 0 ?

Shabarish Ch - 6 years ago

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Yes, but I meant for all values of xx and yy.

Sharky Kesa - 6 years ago

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Hmm.....

Shabarish Ch - 6 years ago

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y can be any value in this case, since only x has to be 0. ((According to x + y = y))

Zaid Baig - 6 years ago

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zero cannot be divided

Dani Natanael - 6 years ago

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zero cannot be divided "by"

Satvik Golechha - 6 years ago

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if x=y then you should not cancell x-y on both sides of equality

Sai Krishna Chary - 6 years ago

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IN STEP 4, YOU CANCELLED X-Y FROM BOTH SIDES AND X-Y WILL BE 0. SO ACTUALLY YOU DIVIDED BY 0 WHICH IS NOT DEFINED. SO, YOU CAN'T PROCEED TO STEP 5. GOOD IF YOU KNOW THIS, IT MEANS THAT YOU ARE GOOD AT MATHS BECAUSE YOU KNOW THE FUNDAMENTALS OF IT. THESE KIND OF QUESTIONS STRENGTHEN YOUR CONCEPT IN MATHEMATICS. I WOULD BE OBLIGED IF YOU POST MORE QUESTIONS OF THIS KIND. I LOVE MATHS AND WANT TO STRENGTHEN EACH OF MY CONCEPTS:)

Kushagra Sahni - 6 years ago

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x = y x - y = 0 But in 5th step we cancelled x-y

Vaibhav Chandan - 6 years ago

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because of division by zero (x-y)=(1-1)=0

Mohamed Abdalla - 6 years ago

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Here (X-y)=0 so we can't devide it from both side so the 4yh step is wrong

MEET PATEL - 6 years ago

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I have objection ! you have said that x=y then x-y=0 then why are you cancelling x-y on both sides?

Kalim Ullah - 6 years ago

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why cant we divide zero by zero?

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That could assume ANY value (i.e. 0, pi, 13, 23523523523,e, you get the point where y,o,u,g,e,t,t,h,e,p,o,i,n, and t are real numbers, etc.)

David Lee - 6 years ago

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x squared - y squared = 0

shivamani patil - 6 years ago

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x = y i.e. x- y = 0. But we cancelled x - y from LHS and RHS in the fourth step, which means you cancelled 0!!! I was in a condition of getting a 'Heart Attack'!!!!!!!!!!!!!!!

Vaibhav Chandan - 6 years ago

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u cant cancel 0 from both the sides in step 4! x-y=0!

Gunjas Singh - 6 years ago

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you must not cancel x-y on both sides as both have value of 0

Aakash Khandelwal - 6 years ago

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Actually it must be: (2-1)^{2} = 2^{2}-2x2x1 +1^{2} =1^{2}-2x1x2+2^{2} =(1-2)^{2} i.e., (2-1)^{2}=(1-2)^{2} =2-1=1-2
=4=2 Hence, 2=1

Shreyans Badjatay - 6 years ago

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0 by 0 is not 1 my friend

Vibhu Baibhav - 6 years ago

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The error is in line 4 x-y=0 It is incorrect for divided with this.

Reajul Haque - 6 years ago

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sir you can't just remove what is spouse to be one of the solutions and say hi everybody the algebra is wrong....

Ahmed Sheweita - 6 years ago

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what if i say 1=1
25-24=41-40
(3x3)+(4x4)-(2x3x4)=(5x5)+(4x4)-(2x5x4)
(3-4)^2=(5-4)^2
3-4=5-4 (taking root both sides)
-1=1

Piyush Patnaik - 6 years ago

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if x=y then x-y=0 we cant cancel 0

satyam mani - 6 years ago

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x-y = 0 You cannot cancel it from the equation

Vivian Sudhir - 6 years ago

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We have seen and it is easily observed that the note posted by Sharky Kea is wrong (I mean to say 1 + 1 is not equal to 1) . The truth is when we solve a equation we actually don't know the value of the variable or variables.But in this case we already have put that x = y so by this we know that x - y = 0 so we can't just cancel x - y on both sides . In case we don't know the value or if x is equal to y or x is greater than y or something else..... In that case we can cancel x - y on both the sides as we don't know the value of it , it may be 1 or 4 or even 0 . But because can't assume that it will definitely be 0 so we can cancel x - y on both sides and then the answer will come to be x = 0 and if we substitute it , it holds true. So, 1 + 1 is not equal to 1.

Utkarsh Dwivedi - 6 years ago

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if x = y , then x-y = 0, therefore you cant use x-y to divide your algebraic expressions

Jay Tio - 6 years ago

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x - y = 0 since 0/0 is not defined... its false

Aakash Amish - 6 years ago

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Division by zero is undefined

Haider Ali - 6 years ago

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You divided by 0.

Eileen Melville - 6 years ago

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In the third step we subtract y^2 from both the sides. Then we get x^2 - y^2 on left hand side. But x^2 - y^2 = 0 as x = y , x^2 = y^2 , x^2 - y^2 = 0.

Arya Ukunde - 6 years ago

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so, we have fallacy in the third step itself.

Arya Ukunde - 6 years ago

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if u remove (x-y) on both side then a condition x is not equal to y should be followed.......so it is wrong.

Vivek Yadav - 6 years ago

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cancelling out the term (x-y) because that means you cancel zero.

Darien Jonathan - 6 years ago

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Step 1 & 2 are..

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x-y can be cancelled when you x-y is Not equal to zero means x is not equal to y

Kanthi Deep - 6 years ago

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in step 4 you cancelled (x-y) on both sides but as x=y that means that x-y = o and any expression divided by 0 is not defined.

Abhisek Mohanty - 6 years ago

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there are more than one problem in your answer the first one when you divide the both side on (x-y) the rule is ( x - y != 0 ) and x = y so x - y = 0 and you can't divide the second one is when you reach to the line before the last one x + y = y so that will be x = y - y that's give x = 0

Wael Fawakhiri - 6 years ago

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Since x=y, x-y=0... if you divide a number by zero it will be undefined, so you cannot divide the equation by x-y.

Marchan Sy - 6 years ago

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Not sure that x-y=0 or not!

Minh Bùi - 6 years ago

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No, we are not assuming. If x=y, then obviously x-y=0

Kushagra Sahni - 6 years ago

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Here one can't cancel x-y from both sides

Tushar Chaudhary - 6 years ago

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No, we are not assuming. If x=y, then obviously x-y=0

Kushagra Sahni - 6 years ago

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U r assuming (x-y) = o which is not the case !!

Karan Nahar - 6 years ago

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Hi Kesa i'm also confused with this riddle.there is an aliter proof also

abhinav anand - 6 years ago

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In step 4, you divided both sides by (x - y) to arrive at x + y = y.

Meaning, there is a division by zero.

James Canaveral - 6 years ago

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On 4th step (x+y)(x-y)=y(x-y), you have cancelled out x-y from both the sides. But according to the assumption made, where x=y => x-y=0. Also 0/0 is undetermined not 1 , so that step is wrong.

Yash Mohan Sharma - 6 years ago

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u can't cancel x-y bcz it is 0.

Harsh Bhavsar - 6 years ago

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you are a master piece as you can divide 0 by 0

Uttaran Choudhurry - 6 years ago

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At the fifth step, we arrive at the result- x+y=y.Let us think at once, at what values of x and y, can this be true ?only when x=y=0.This is the only solution to x+y=y.If this solution follows , we can never get the result 1+1=1.This is the fallacy.

Dheeman Kuaner - 6 years ago

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x-y=0

João Victor - 6 years ago

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x-y=0 => 0/0

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you just cancelled two zeroes respectively from the lhs and the rhs in step 4. This cant be done

Udayan Joshi - 6 years ago

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in 3rd step there is (x^2-y^2) at l.h.s. & in next step it is written as (x+y)(x-y),but it is not applicable for the equal numbers which is the condition given in 1st step....

Utkarsh Tyagi - 6 years ago

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interesting! I can't find it

Nguyen Thien Vy - 6 years ago

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x=y, therefore x-y=0.

Sharky Kesa - 6 years ago

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The element is zero shock swallow does not participate in the multiplication operation

ibrahim çakır - 6 years ago

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x+y ≠ y

Hans Ramírez - 6 years ago

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in the 5th step

math man - 6 years ago

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x-y/x-y = 0/0 math error

Prateek Rai - 6 years ago

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(x+y)(x-y) = y(x-y) only proves that 0=0 x-y cannot be cancelled out as we usually do

Naveen Mathew - 6 years ago

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(x-y) can not be divided from both sides as x=y makes it divided by zero.

Tarak Das - 6 years ago

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x^2 =y^2 doesnot imply x=y

sunitha bhadragiri - 6 years ago

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x = y

x - y = 0

In the fourth step you divided by (x-y), or 0. And when divided by 0, it should be 0 = 0 not 1 + 1 = 1 :)

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x-y = 0 & you cancelled 0 on both sides ( 0/0 is not 1 , but undefined).

Anchit Virmani - 6 years ago

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In the 4th step, (x-y) is on the both sides. dividing (x-y) by (x-y) gives 0/0, which is the indeterminate form. That is the fallacy

Eshan Abbas - 6 years ago

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since x=y, x-y=0,and in the next step the division isnt possible because division by 0 is not defined in mathematics

Benson Thomas - 6 years ago

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Substitute numbers from the beginning and then you get the fault. :P

Shreya R - 6 years ago

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x-y=0

Ritesh Manna - 6 years ago

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x=y x-y=0 so (x+y)(x-y)=y(x-y) (x+y)(x-y)/(x-y)=y as (x-y)=0 (x+y)(x-y)/0 which is not exist

saranya Naha roy - 6 years ago

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you cannot cancel x-y to both sides since x-y = 0. any number divided by 0 is undefined.

Cabug John Carlo - 6 years ago

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when you cancel x-y in LHS with RHS,it directly means that x not equal to y,but then you are putting x=y in next step!

RamanDeep Singh - 6 years ago

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divided by zero

Marjun Fernandez - 6 years ago

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In step 4 you have cancelled 0 from both sides which is not possible

sagnik ghosh - 6 years ago

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YOu cannot cannot 0 both sides.

raja ragh - 6 years ago

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u can't divide by x-y since x -y = 0

Austin Seiberlich - 6 years ago

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x - y = 0 and any no. divided by zero is infinity so,we can't cut x-y from both sides.

Mayank Mahajan - 6 years ago

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Take a note from x=yx=y The false statement is when dividing both sides by the difference of x& y where it is indeterminate with denominator of x-y=0.

John Aries Sarza - 6 years ago

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cannot divided by 0 two sides of equation in step 4 (//because x=y so x-y=0)

Phunn Boonchouchouy - 6 years ago

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x+y=y is the fallacy

Sonika Kumar - 6 years ago

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Division by zero. Since x = y, x - y = 0. We cannot use the Cancellation Law of Multiplication for a factor of zero.

Jaybee Penaflor - 6 years ago

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the eqation (x+y)(x-y)=y(x-y) has two solutions ,first one is (x+y)=y and (x-y)=0.Which gives x=y,the right solution.

Vishal yadav - 6 years ago

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x-y, since x-y=0, dividing any number by 0 is undefined (0 by 0 is indeterminate).

Bernard Ian Nieto - 6 years ago

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because x=y so x-y= 0 => in step 4 you can change both sides to 0

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You cannot cancel X-Y until X=Y....

Madhukar Thalore - 5 years, 12 months ago

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cancellation of (x-y) on both sides is a mistake

geetha kumar mamidisetty - 5 years, 12 months ago

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If x=y then (x-y) =0 and hence it cannot be divided on any side.

Gautam Singh - 5 years, 11 months ago

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x-y=0, in step 4 x-y can't be eliminated

Radha Krishnan B - 5 years, 11 months ago

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x=y

Aya Mohamed - 5 years, 11 months ago

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From (x+y)(x-y) = y(x-y) to x+y = y, you divided each side by (x-y), but since you cannot divide by 0, this only applies if x-y does not equal 0, and since you set both x and y as 1, x-y does equal 0, which makes the equation invalid.

Anthony Ng - 5 years, 11 months ago

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x=y => x-y=0 => can't divide ( x-y ) in line 4

Nguyên Nguyễn - 5 years, 11 months ago

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dividir entre cero

Oliver Garcia - 5 years, 11 months ago

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You cancelled x-y with each other. what if values of it is 0? Cancelling of 0/0 is not 1. Btw, result is x=y=0

M.s. Saggoo - 5 years, 11 months ago

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since x-y=0 you can't cut x-y on both the sides of step no.4

Aakash Khandelwal - 5 years, 10 months ago

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This should have been framed in a form of a question.

Anuj Shikarkhane - 5 years, 10 months ago

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since x=y as stated in the problem, dividing both sides by (x-y) will result in an undefined equation as (x-y) = 0. (x+y)/0 = Undefined so the equality does not hold. <It is equivalent to saying that 1/0=2/0 clearly undefined>

Andrew Yu - 5 years, 10 months ago

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as per you second last equation, x is multiple of 2y .. so "x" never is equal to y..

Muhammad Ahsan - 5 years, 9 months ago

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well.. (x-y)=0 so,, no

RuBa HuSsein - 5 years, 9 months ago

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you have just factored 0 , there are many solutions .. just like 9 x 0 = 0

okijo setsu - 5 years, 9 months ago

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x-y is 0.Cannot cancel a 0 term

Tapan Saraph - 5 years, 7 months ago

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x-y is not 0. you can not cancel a 0 term

Pratham Sharma - 5 years, 7 months ago

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x=y x =y means

xy=0 x -y =0

in step 4 you are dividing the expression by zero which is not possible . this is the fallacy

U Z - 5 years, 7 months ago

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You should watch forth step you ignored x-y ... It Means u r handling it like a real number...but if you transfer both x-y in one side you will see that u have made 0/0 undefined form......

Puneet Mehra - 5 years, 7 months ago

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its wrong when x + y = y, x=y -y or x=0 so you are dead wrong man

Shashank Madhusudhan - 5 years, 7 months ago

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x=y implies x-y=0.In step 4 we have divided both sides by 0.So,it's 0/0 which is undefined.

Kapil Chandak - 5 years, 7 months ago

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That's not possible

Pratham Sharma - 5 years, 7 months ago

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in 4th line, you cannot cancel zero (x-y=0) with zero of other side.

Uzair Awan - 5 years, 6 months ago

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(x-y) = 0. You took 0/0 = 1, which is actually indeterminate.

Ashish Menon - 4 years, 2 months ago

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(x + y )(x - y) = y(x - y) can yield to (x+y) = y only when x not equal to y.

Chenchu Krishna - 6 years ago

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since x=y,x-y=0 in 4th step u have divided by x-y=0 which is not allowed

Maninder Kaur - 6 years ago

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here, given that x=y and it means x-y=0.... and in 4th step we cannot cancel out (x-y) from both side... so this is totally wrong

Preyans Raval - 6 years ago

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Why x=y if x=y then at last what is the necessity that x+y=x

Subrat Panigrahi - 5 years, 9 months ago

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If x=yx=ythen xy=0x-y=0 so in the 4th step you are factoring as (x+y)(0)=y(0)(x+y)(0)=y(0) and in the the 5th step you are dividing both sides by 00 and taking the result as 11 which is not allowed

Abdur Rehman Zahid - 5 years, 6 months ago

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This talk is wrong, because it can not be divided by zero to zero, or equal to, this clowning

Ahmed Zizo - 6 years, 5 months ago

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Many remarkable things are discovered as a result of clowning :)

Silas Hundt Staff - 6 years, 5 months ago

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Is clowning the same as trolling, just more mathy?

Alexander Sludds - 6 years, 5 months ago

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@Alexander Sludds I'm curious too, whats clowning?

A Former Brilliant Member - 6 years, 5 months ago

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@Sharky Kesa Hi This note is similar to my question 'Is it True?'.. check out https://brilliant.org/community-problem/is-it-true/?group=enKxDb2d6cg4&ref_id=201435

Ritu Roy - 5 years, 11 months ago

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Well, technically, the problem is similar to my note. I posted this over 5 months ago, Eddie had reshared about 3 weeks ago and it became a hit. Before, it wasn't.

Sharky Kesa - 5 years, 11 months ago

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We can cancel only non zero common term in both sides of an equation

arun kumar - 5 years, 11 months ago

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