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From: mrjames113083
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  • The real way to prove 2=1. Write it on paper to understand better.

    Take 2 as 2/1. Then multiply this by infinity/infinity (anything divided by itself is 1, so the 2/1 will stay as it is since you are multiplying by 1). Infininity x anything is just infinity. Therefore 2 x infinity is infinity and 1 x infinity is infinity. Therefore 2/1 x infinity/infinity = infinity/infinity = 1.

    BOOM

  • If X=Y, then XY is the same as X^2, so X^2 - XY = 0, so you divided 0 by 0 at the end.

  • dividing by zero

  • i wanted to be that guy until you said youd be mean to me and we have to be in a classroom together til june so ill be quiet now :D

  • im assuming he was challenging you guys to find the error i think he already knew it was wrong

  • Nearly all false proofs result from the fact that you are dividing by 0 at a point. 

  • The problem is on step 3. In step 3, both sides subtract 2XY. In the left hand side, 2X^2 - 2XY actually is equal to zero. In the right hand side X^2 - XY is equal to zero too. Since both sides are equal to zero, the factoring in step 4 become meaningless as any number times zero will result zero. Thus this video is a gabbage.

  • you are all idiots: X^2-XY is one of the last steps and if you can remember that X=Y so what you are saying is that (Y^2 -YY) which does = 0 so, you just proved that 0=0 well done.

  • Try this on for size: Assume x does not = 0... though it is implied in this next step. Let x = 1+1+1+...+1 (x times) [Multiply both sides by x] x^2 = x+x+x+..+x (x times) [Take the derivative of both sides with respect to x] 2x = 1+1+1+...+1 (x times) [By our original definition of x, substitute] 2x = x [Divide by our non-zero x] 2 = 1 What's the mistake?
  • @DDOGGSWINCHY

    Equivocation -- you defined x to be a constant, then differentiated the functions f(x)=x^2 and g(x)=x+x+... (x times). Using the same line of reasoning and treating x as a constant throughout leads to 0=0.

  • it has nothing to do with division by zero... it has to do with the fact that both sides of his equation were multiplied by zero. x*0 = y*0 for any values. he could've made his claim without actually "dividing by zero"; if 2x = 1x (for any x that isn't 0), 2 = 1. the catch is that in this case... x = 0. funny stuff, youtube mathfolk. i really enjoy ignorant folk using big words like "invalid", "thus", and "fallacy".

    troll (correct troll, i might add) out.

  • Yu ARE allowed to assume y=x just as if u said ricky can lift the same amount of weight as john. the problem is that if y=x than y-x=0 and you can't divide by zero. Anything divided by 0 is undefined.

  • x^2-xy=0, you can't divide by zero ya dunce XD

  • A you divided by zero. B you should know that dividing out a variable creates a loss of values

  • Division by zero is an invalid operation, and thus the proof is a mathematical fallacy.

  • you cant divide by 0 x^2 - xy is equal to 0

  • So you just proved that 2(0) = 1(0). We knew that.

  • x^2=xy, so x^2-xy = xy-xy which is 0.

  • WOW THIS IS AWESOME!!!! I'VE NEVER SEEN ANYONE DIVIDE BY ZERO SO AWESOMELY BEFORE I WATCHED THIS VID!!!!! WOO-HOO DIVIDING BY ZERO!!! YEAH!!!!!!

  • Here is the issue: you divide by (X^2 - XY), but since X^2=XY, you are dividing by zero, which is not possible.

  • the only problem was the factoring they would factor like this 2x(x-y)=x(x-y) divide by x-y and you get 2x=x which is only true with 0 but any other number will work like 1=2 or 2=4 or pretty much any number multiplied by 2 everything else is mathematically sound.

  • you cannot divide x squared minus xy from each side. it's so simple.

  • @jmfooter14 that's the thing about math it IS simple.

  • Oh my god! my brain just melted.

  • It is because you are dividing by zero. Any integer for x will result in a divide by zero error.

  • HOLY FUCK I'M THE 6,666th VIEWER.

  • @xxMrSaGgYxx are you the antichrist?

  • You divide the last step by 0!

    As all mathematicprofessors and all scentists know,

    ONLY CHUCK NORRIS CAN DIVIDE BY 0!

  • 2 (mod 1)=1

  • HAHAHA...... u took benefit of concept 2*0=1*0. but here we can"t do 2=1*0/0 as 0 divided by o will become indeterminate. BUT u have hidden the 0 here in algebric form of X^2 - XY. now u cancel X^2 - XY/X^2 - XY =1 which is wronge BECAUSE X^2 - XY = 0 as u assumed before X=Y. it wud have worked in any other case when X not equal to Y.

    liked the video.

  • in the last step, you are dividing by zero

    since x=y, and by allowing the division of the factor (x^2-xy), you are committing a fallacy.

  • you divided by zero its undefined

  • Beautifully done!  And a very entertaining way of dividing by zero.

  • since x=y ,x-y=0,x^2-xy=0,we cannot divide by zero on boyh sides

    

  • (X^2-XY)=0. In the ladt step, you divided by (X^2-XY), that means you divided by 0, whith you can't do. That what's wrong.

  • my head hurts... i suck at maths XD

  • I got it! In step 4, all = 0. And then it's wrong in step five to take that away! So it goes from 0=0 (which is right) to 1=2 (which is wrong). Good trick!

  • i hate when titles have lies in them xD

  • You can presume x=y... But once you random assign values to it... which you did by applying it to the equation 2=1.... Is wrong, you cannot enter unknown/unset algebriac values into a set equation...

  • If X = Y, then X^2 - XY is the same as X^2 - X^2, which is zero. Then you divide by that, which is division by zero, which is ILLEGAL.

  • Your mistake was that x*x=x*y so actually x*x-x*y=0 You divided both sides with zero and that is the mistake because you cant devide both sides with 0.If we could do that it would ment that 1=2=3=4=5......=123123=..... How?this is how:

    x , y are some numbers( they can be any numbers)

    If we say that x=y we can devide both sides with any number and the equivalation will stay the same .If we devide both sides with zero we get this 0=0 and that is true.With the law of implication x=y, 1=2=3..

  • failure is where u divide by (x^2 -xy). as x = y, that equals 0. dividing by zero!!!! fail. good trick tho

  • 2(X^2 - XY) = (X^2 - XY) is possible only if the (X^2 - XY) is equal to 0. So we've got that (X^2 - XY)=0 you cannot devide with 0. There is the fail.

  • they are not kidding you man, but what you did is that you used the definition in the wrong way!

    the definition says : a.b =c.b then a=c iff b!=0 ( b not equals to 0) and you assumed that x=y and you divided by x*x - x*y => 0 and you can't divide by 0

  • if x=y then x^2-xy =0 and you cannot divide by zero you should have infinity=infinity as x^2-xy tends to zero

  • The mistake is the division by x^2-xy. Since x=y, this is the same as dividing by xy-xy, which is 0. And that always seems to be the fallacy in these types of math teasers. Cool video.

  • Okay, I really like this question, so first off, I would like to thank you for posting this video up. Now the flaw: in step five, when you divided both sides by (x^2-xy), essentially, you are dividing by 0 because if we sub in "x" for "y" (stated at the beginning), we get the following:

    (x^2-x*x) = (x^2-x^2) =0

    Therefore when you conduct step five, you are, in essence, dividing by zero, which is unallowable. Nice video though, I'm looking forward to more. Thanks.

  • Okay, I really like this question, so first off, I would like to thank you for posting this video up. Now the flaw: in step five, when you divided both sides by (x^2-xy), essentially, you are dividing by 0 because if we sub in "x" for "y" (stated at the beginning), we get the following:

    (x^2-x*x) = (x^2-x^2) =0

    Therefore when you conduct step five, you are, in essence, dividing by zero, which is unallowable. Nice video though, I'm looking forward to more. Thanks.

  • It's easy..in the final part you divided by 0..because there is 2(X²-XY)=(X²-XY), in which clearly you cant divide by X²-XY..

  • geez...

  • well heres how you can see the flaw, replace x and y with a number like 2, because its easy to work with (im doing the lines by the steps)

    2=2

    4=4

    8=8

    0=0

    factoring : 2(4-4)=(4-4) {still true}

    heres the flaw: when you subtract x^2-xy you get 0, and you cant divide by 0

  • your problem is actually that x squared and xy are the same since x and y are equal. so the equation x squared - xy equals 0; at the end of the equation you divide by x squared - xy, which is of course 0; which is of course mathematically illegal. you will be fined. maybe you should think of that before you break the law, son!

  • Isn't x^2 + x^2 really x^4, not 2x^2?

  • you can't divide by x^2-xy it's equal zero since x=y so x^2-x^2=0

  • X-y = 0, dividing by zero is irrational. therefore your logic is false.

  • Nice trick, reminds me of proving 0.999....=1. Do you know that one?

    Yeah, (x^2 - xy) = (x^2 - x^2) = 0 (x = y). So, of course, dividing by zero produces crazy things.

  • you are assuming that x^2-xy DOESN'T EQUAL ZERO on the last step. because any # divided by zero is undefined.

  • If x=y then x^2-xy=0. You cannot divide by 0, therefore the argument is flawed.

  • Comment removed

  • LOL...i hope your jk

  • No seriously tell me why I should assume something that is absurd?

  • Dude, when it is "assumed" that x=y, we aren't saying the letter x "is" the letter y. x and y are representations so saying x=y isn't a logical fallacy or absurd.

    It's like saying I have two different symbols that represent the same quantity. And that being the case, it's mathematically correct to say those two symbols equal one another.

  • ok now I get it

  • @vitalsigns1

    in the simplest way to say this possible, you're stupid

  • although your videos are pretty good brainteasers, i have to say, will you ever do something that isn't essentially pre-algebra? i mean, sure, these are pretty fun, i guess, but after a while they get kinda boring... -.- just saying... if you could get some geometry or even some pre-calculus tossed in, then i would appreciate you videos a little more. but still, for someone who might not be so great at math, your videos are pretty good rack-your-brainers. =)

  • Reminds me the fact that

    n∞ = ∞

  • You said that x=y. So when you say divide by "(x^2-xy)" you're essentially saying x^2-x^2 or y^2-y^2, these both equal 0 (same number - same number = 0). You can't divide by 0, it just doesn't exist. There in lies the problem <3

  • u cant to 0/0 doesnt work

    x-1

    over

    x-1

    this isnt 1 cos it is 0/0

  • btw dudes, he knows theres a mistake, he wants u to find it!

  • i think its cause you divided by (x^2-xy), you can't do that because if x=0 then you just divided by 0 in which case this won't work, to fix this you need to assume x isn't 0.

  • guess your gonna have to ask jacob

  • lololololol

  • Since X = Y, (X2 -XY) = 0, and you CANNOT DIVIDE BY ZERO :)

  • also...................

    there are people that dont know maths...

    you have not to post videos like that because people then will say things like...

    "Oo maths are wrong....."

  • AHHH NO MORE MATH MY BRAIN HURTS!!!

  • the last step is WRONG!!!! x^2-xy=0 . no matter what values x has . lets say x=5, then y=5 so 5^2-(5)(5)=0 , so dividing by x^2-xy is not correct. in mathematics any number divided by 0 is undefined. (good try though : D)

  • @PNDeads To be fair, division by zero is not always undefined: it depends on what you are up to. Often in calculus, depending on the limit, it equals positive or negative infinity. :)

  • @PNDeads So it is a proof for "any number divided by 0 is undefined", not for "2=1".

  • x=y

    so x=1; y=1

    x-squared= 1

    xy=1

    1-1=0

    and you cannot divide by 0!

  • Yeah funny!!

    I think that everything is correct. except the LAST Step that is wrong!

    Because you don't have the right to divide by

    (x^2 -xy) because in case where x = 0 it give 0/0 which is undefined

    But not sure . . .

  • Assuming that x = y is the fault, as x being equal to 2 and y being equal to 1.

  • We can state that anything to the power of zero will always equal 1, any given number^0 = 1, so working backwards, we can logicaly state that ^0rad1 = any given number. Now after much thinking and unnecessary government funding, top mathematicians can firmly state that numbers 1 and 2 are in fact "any given numbers". Therefore, we can definitively state that 1=2

  • Because x cannot equal 0 this proof can be proven false

  • meow !!

  • делить на 0??  оч смешно

  • WAIT a second...

    Since we know Xsquared is equal to XY, why in step 3 can the left side of the equation not be changed to 0? 2Xsquared subtract 2XY would be zero...

    The right hand side would also be zero XY subtract XY is zero (leaving Xsquared) and Xsquared subtract XY is also zero...

    ARGH! Actually this sort of proves my other comment about X not equalling Y incorrect.

  • Surely at the beginning... X never equals Y? Maybe?

  • x = 1/2 ?

  • ur problem happened right at the start, u cant assume x=y - because if u drew this line ona graph then they would both be exact the same number and not 1 and 2 - therefore it is just a silly mistake - did u make this mistake on purpose just to make this video?

  • Like many people don't understand, I am allowed to assume x=y. That's a perfectly legal mathematical situation to assume at the beginning of the problem. As long as I always assume x=y then I'm fine.

  • @mrjames113083 i'd love you as maths teacher, mine had no personality what so ever.

  • @mrjames113083

    Yes you can assume whatever you want in the begining. True enough.

    But you must follow the assumption as TRUE until the end right?

    So X = Y means X*X = X*Y, so BECAUSE OF YOUR ASSUMPTION (X*X) - (X*Y)=0

    and you can NOT divide by zero. Am i right?

    So the division by zero (witch of course is a mistake) creates the paradox.

  • @mayarrow Why not?

  • @mayarrow Did you write this comment to purposefully portray yourself as a moron? The mistake is dividing both sides by x^2-xy. This is impossible as x^2-xy = 0.

  • Hey Mr James : )

    I'd just like to ask out of curiousity, if you have any further math qualifications since leaving high school. If so, what are they?

    I ask this because you seem to have a telent for math.

    Please leave a comment above mine as I'd like to know. Thank you.

  • I have my BS in Mathematics. I have one year professional teaching experience and continue in my career as a math teacher.

  • My Physics teacher is also a big lost fan... what's with numbers, that makes people like lost?? or what's with lost, that attracts numbers likers ??? hmm...

  • @mrjames113083 okay for the 1000 time a day i see videos like this.. OKAY SO you divide by (x2 - xy) x2 = x.y so that means you divide by ZERO .. seriously... every video of 2=1 0=1 or so is the same..everyone divides by zero .. you are BULLSHIT , im sorry , im really , really sorry

  • @mrjames113083 Eh, that don't mean nothing. I have one of those BS in mathematics things, and I come up with garbage that's sloppy and full of errors too.

  • That's why you shouldn't divide by zero.

  • It comes when you factor out the equation. You take the two and move it to the outside, as if you were going to multiply times two the equation inside of the brackets. However, you didn't devide the 2 in with the equation, you're changing it, and making it appear at the end you're left with 2=1, when in reality, you have to devide the WHOLE solution by (x2-xy), thus, in reality, the real solution is

    0=0.

    I think. Dare I say there are to many... VARIABLES. Ohhh, that's funny...

  • lol

  • Comment removed

  • if x=y than x² = x*y

    so x² - x*y= 0

    but its not allowed to dived with 0 :)

  • any number divide by 0 will get infinity...

    but 0 divide by 0 willl get 3 answers:

    1 or 0 or infinity..

    because:

    a) any number/0 = infinity

    b) 0/any number = 0

    c) when two same numbers are divide each other, the result is 1.

    anyone..correct me if I'm wrong.thanks.. (^^,)V

  • I dont know y u have put my explanation as spam???? You asked the mistake and I proved that...

  • I didn't mark it as spam. Anyone can spam a comment. If I didn't like a comment, I have the authority to remove it. Obviously I didn't.

  • yes..we can spam a comment actually..

  • x=y? not possible!!!!!

    if they are diferent letters they represent diferent numbers

    i am 14 years old and i know that

  • and you are retarded

  • just keep silent pls

  • I got the simpler version ...

    0 = 0

    2 * 0 = 1 * 0

    Divide both the sides by 0 to get

    2=1.

    This is the actual error committed in the video, For sure. Because X = Y is the primary assumption. So X² = X.Y goes 0=0. So this is mathematically wrong because we cant divide anything by 0. Hope this answers the mistake.

  • immortalnoob is right this guy cant factorise.

  • this guy cannot factorise.Check step 4 again and you wil see that he could take an extra x out of the brackets on both sides

  • There is no mistake. Only in the final conclusion. Because X^2- X.Y will be always zero because X=Y. And 2 times 0 it´s equal to 1 times 0. This problem don´t have the solution of 2=1 but of 2/1=0/0 which is an indetermination, in this case any X you chose wil be a solution.

  • yaa

  • we know, since x=y, that x squared - y equals zero...no dividing by zero! It's not allowed. Thus, the error.

    p.s. I love your LOST videos...way better than Seanie B, because you upload them faster and just give us the good stuff, not a long boring recap of every detail!

  • youre a complete retard..

    you are saying that x squared - y =0

    lets say both x and y (because they are equal) are 5

    25-5 doesnt equal 0 it equals 20

    i dont know the problem with the equation in the video, but i know there is definitely a major flaw in your crappy logic

    now i am not usually this rude, but you pissed me off about your comment on seanie b's videos. he makes such in depth recaps because some of his vieweres dont want to hear irrelevant topics lik james puts in his vid

  • That was to me?

    It´s not X^2-Y=0

    It's X^2-X.Y=0

    You need to go again to school.

    I don´t know if someone understood what you were trying to say with Seanie B videos...

  • wasnt talking to you dickweed..

  • doctorB92, Thank you for catching my error. I am embarassed that I made such a simple mistake. Here, I have since fixed the mistake:

    we know, since x=y, that x squared - xy is essentially x squared - x squared, which equals zero...no dividing by zero! It's not allowed. Thus, the error.

    p.s. I love your LOST videos (No offense is meant toward Seanie B or any of his followers.)

  • sorry bout my rude reply, but i just got finished replying to someone who left a gay ass comment on my channel

  • this is all based on the assumption that x=y. He begins with x=y and adds and multiplies variables to both sides of that equation and eventually comes up with 2=1. Unfortunately, x does not = y and that is the error.

  • "Unfortunately, x does not = y and that is the error. "

    That is not the error, if he assumes that x=y, than x=y.

  • 1/0=2/0

    doesnot mean 1=2

    ok dude

  • it s not 1/0=2/0 it s 1/1 = 2/1 !!

  • you're wrong 1/1 is a whole 2/1 is half a whole you're saying 1= 0.5 which is incorrect

  • Comment removed

  • my mistake

    but thats not trrue either

    1X0 = 2X0

    does not mean

    1 = 2

    because x2 - xy = 0

    check that

  • You are quite fun to read 1x0=0=2x0=nx0

  • a one legged man cannot stand on his head

    0/1 not possible

  • Zero divided for 1 person... Person gets zero apples :o) So your answer is zero.

  • lol to tell you the truth, i didnt watch the whole thing before, but just guessed because i assumed it was the same question

    the real answer is that x is not equal to y, so xsquared is not equal to xy

  • I'll admit you got me to think though

  • Oh SHI-

  • I know the Solution and the wrong thing.But i don t say it. Do not be jerks. Leave them to find the solution alone...

  • you cant divide by 0. yay!

  • Wouldn't you think it's a huge waste of time just to prove that 1 = 2?

  • the 0/0 indeterminacy. Actually you guys are all dumb. It's the assumption that 0/0 is equal to any one number that's wrong. 0/0 is effectively equal to all numbers(including 2). The problem is that you assumed that it is only equal to 1. Since x=y, then x2-xy/x2-xy is 0/0.  However, this does not mean that x2-xy/x2-xy is equal to 1. The typical explanation is that you can't divide by zero. You can; you just can't assume that this 0/0 is equal to one.

  • Ironically, all the explanations on this page are wrong. 1. You can divide by squares accurately. 2. This is not a proof of 0=0. It is a proof of 0/0 = any number. 3. x and y don't have to be equal to zero. x2 - xy has to be equal to zero. Which is shown in the beginning by the assumption x=y. 4. You can, in fact, divide by zero. The problem is when you assume that x/0 is equal to some specific number. When x does not equal 0, x/0 is equal to + or -infinity. When x=0, x/0 equals any number.

  • Division by zero is undefined...It is not any number or +,- infinity.

    If you are taking a limit then that is a different problem. There are no limits being taken here.

  • Comment removed

  • Actually, it is possible to divide by zero. In many contexts, it is important to recognize this fact. 0/0 is the classical mathematical exploration called the indeterminacy, which I explained below. In other cases, like some aspects of quantum physics, it is important to recognize that any number divided by zero is infinity. I understand why you may shrug off the concept and simply decide that you cannot divide by zero. But that is an unfounded and incorrect generalization.

  • No it is not. It is undefined. Only when you are taking limits is it an indeterminate form

  • The video is about arithmetic. The real numbers are a field. Division by zero is undefined in a field.

  • I guess that is a fair enough claim. However, it is necessary in many fields beyond simple arithmetic, making it an important philosophical point that it can be done. Although you are correct that it is usually done in the context of some limit, when used in many physics-based applications, it is used outside the context of limits as well. For most mathematical purposes we assume that it is undefined, however doing so is mainly just hair splitting as a result of it's unnecessary results.

  • For instance, in a field if we assume division by zero to have a result, it must not only be + infinity but also - infinity. This is extraneous in most broad math contexts. However, when dealing with gravitational singularities, it becomes necessary to consider x/0 an appropriate maneuver.

  • step 5

    you can cancel the square by roots

    if you dont understand then im not bother to describe

  • dont cancel square by divide

    cancel square by roots ONLY

  • The proof I've provided in my last comment cannot be denied. As you started with assumption that X=Y so in the whole process we can use both of them at each others place. And when u do that in step 4 both sides go to zero. It actually proves mathematical fact that 0=0 not 2=1

  • Step 4: 2(X2-XY)=(X2-XY) (Read X2 as X square) As X=Y according to our fist assumtion,

    So 2(X2-X2)=(X2-X2)

    or  2*0=0

    or 0=0

    Thats what it's all about. In step 4 its just like both sides r multiplied by zero and he divides both sides by zero to eliminate it which is not possible.

  • Step 5 is wrong!!! It is impossible to divide by 0. Before you post any more proofs you should make sure they are correct!!

  • Wow. Someone doesn't listen to directions. Read the side box next time or watch the video until you hear my disclaimer saying it's incorrect.

  • dood that's so cool ur awesome

  • the only way 2(X2-XY)=(X2-XY) can be true is if X and Y equals zero....

    that would make 2(0)=(0) or 0=0

    NOT 2=1

    I win....

  • nooo ur so stupid it equals 1 i showed this to my math teacher its correct

  • pfft lame... chuck norris could divide by zero >.>(awesome video tho) =)

  • the step when you divided by

    (x^2-xy) can't be done because

    you are dividing by zero.

    (x^2-xy)=0 since we assumed

    that x=y; therefore 2 is not

    really equal to 1.

  • right.

  • I know an even better proof! 2=0!!!

    Given a=1, b=1

    Thus a+b=2, and a^2+b^2=a+b

    Substitute, and get a^2+b^2=2

    Factor to get (a+b)(a-b)=2

    Plug in the original numbers, (1+1)(1-1)=2

    Simplify, (2)(0)=2

    Multiply, and you get 0=2

    I CAN'T FIND THE ILLOGIC!!! WHERE IS IT???

  • a^2+b^2 does not factor into (a+b)(a-b), you would need to factor a^2-b^2.

  • All you have to do is substitute a number for x.

    2(x^2-xy)=x^2-xy ... substitute "x=3, y=3"

    2(3^2-3*3)=3^2-3*3

    2(9-9)=9-9

    2(0)=0

    0=0

    Since you divided by zero, it screwed up your maths. You're not allowed to do that.

  • do you think people are so stupid?

  • when it comes to math...the average person kind of is.

  • O, forgot

    Unless you follow the concepts of transreal arithmetic you can't divide by zero.

    But if you do follow transreal arithmetic than it equals a form of nullity and than the equation still doesn't evaluate to 1=2