I love that depending on how you define the result of an infinite sequence, you can "proof" 0=1, 1=2, -Inf = +Inf and so on. It's the magic and horror of working with infinity.
Good points. You understand what's going on here but most people are stumped. Please see if you can fool many others by sharing and promoting this video. Thanks a lot.
Sir to take out 1 out of the 1st bracket it is essential to also subtract 1 otherwise it is impossible to take out 1 out of the 1st bracket and do grouping. Therefore without subtracting 1 when grouping makes your 3rd step invalid. By virtue of taking out one and grouping you are subtracting one automatically . So you cannot have a one standing alone +sum of infinite 0s. You are obliged to subtract 1 immediately you start doing the grouping. i.e (1-1)+(1-1) = 1+(-1+1)-1 You must immediately subtract 1 when you take out 1 out of the first bracket and start grouping.
I was just thinking that...PEMDAS more or less destroys his proof. Probably more accurate to say the sum of series is zero _or_ one if that first 1 isn't grouped.
@@sdwvxic-1711 infinity isn't number you can multiply. And if it were possible infinity * 0 + 1 would be equal to 1 because anything times 0 is equal to 0. Thus adding 1 would make it 1.
@@KiemPlant actually if i remember well if you have a serie that limit is 0 and another than goes to infinity and multiply them, the resultant serie can go to anything and you have to do more calculation to find its true limit (sry i don't know english maths terms very well) 0 x infinity can be any number in this case, so we say it is not defind
I don't hate math but my teachers in high school made me hate it. Students who are bad at math were scared to ask questions from them because they always scolded us for being slow learners in math and embarrass us in front of the class forcing us to solve problems on board, even though we were trying our best to understand. Having a teacher like you, makes me want to say that learning math is fun! ☺️ And you explained it in a way that it isn't hard to understand. Thank you!
search "eddie woo" on youtube, he is practically the best math teacher on the planet. He's got everything from basic math to advanced calculus. I currently take AP Calculus AB and im literally the top student just bc of him. He is amazing, He's also done a ted talk as well; he is worth checking out.
THIS, I learn at a convent jr.college here in India and this is the same problem with me, I wish there was a better teacher who wouldn't embarass you in front of the whole class for asking some basic doubts
TO PROVE 0=1 PROOF:- LET 0= x-1 Acc. To Question, x-1=1 x=1+1, x=2 Where, x-1=0 And We Finded x-1=1 And, x-1-0=0-----------eq(1) x-1-1=0---------eq(2) Divide Eq. 1 and 2 x-1-0 upon(by) x-1-1 it will be -0 upon -1 then -1 is in divide form Take It to the RHS and It Will be +ve...Hence Proved 0=1
@@tusharkumarraj6066, In my opinion, he is wrong. He just didn't write "-1" which has to be in the equation but it can be so far away that he can never write it.
hate to be that guy, but I can disprove this - i'm not sure if this is what the guy who objected near the end said, but this is how I do it: in the second step, each bracket ends in a -1. this series goes on infinitely, so the theoretical 'last term' would be -1. so in the third step, after all of the brackets of (-1 + 1), there has to be a -1 at the end, because the series cannot 'end' in a +1, it 'ends' in a -1. so the +1 at the start and the -1 at the end will cancel out, totalling 0. this added to all of the other brackets still gives 0. again, hate to be that guy, but it had to be said.
@Kian Saliany LOL but they are only good if they can find out where mistake is instead of that annoying kid in the class who doesn't know a shit but just wants to proove the teacher wrong
Me: Hey dad, can you give me 0 dollars? Dad: Sure why not? Me: Thanks, so give me 2 dollars. Dad: Why? It should be 0. Me: 0 is equal to one and one is equal to 2!!!!!
Yeah, this is why calculus is always so specific about limits; if it were to say “infinitely small”, everything just breaks. Infinity is necessary, yet also the breaking point of all things maths
So you're saying if a guy had 0 dollars, he would have 1 dollar. 🤔Thanks that makes me 1 dollar richer... ;) Wait... What if I make a bunch of bank accounts with 0 dollars in each. Thanks John Hush for the idea. ;)
but if 0=1 & 1=2 & 2=5 as he has proven, that means youll make 5 dollars, and if you divide this 5 dollars to 5 one dollars then youll have 5 5 dollars, and so on, then youll have infinite money
Not me being late 9 years. And this video just popping out in my recommendations. Having you as a teacher would be a blessing for everyone. By far the best teacher!!
Lot's of good thinking in the comments. But I have yet to find the mathematically "correct" explanation. So here's my very long and detailed attempt at explaining the official mathematical reason this proof is invalid. Hope y'all enjoy. The first little complexity comes up in the first step where he says 0 = 0+0+0+0+... Depending on the field of math, this can be right or wrong. An infinite number of zero's is not necessarily 0, it's undefined until given further context. Just as how 0 * infinity is considered undefined, 0+0+0+... and infinite number of times is also considered undefined without further context. Now within the context of series (Real Analysis) he's right. The infinite series of 0's is axiomatically defined as 0 (meaning when Mathematicians write the "rules" of series, they make it true by rule that an infinite series of zeros is zero). This is done for some obvious reasons. Otherwise any series could be made undefined just by adding a bunch of zeroes. More precisely, and most importantly, an infinite series of 0's when writed 0+0+0+0+... (notated as "Σ0") is convergent. This means as you add more and more terms, the sum converges to one value, zero. i.e. If you take each term one by one, you get 0, then 0+0= 0, then 0+0+0= 0, then with the next term added 0 again, and again, on and on. You always get zero, so it makes sense the series as a whole should be defined as 0. It is for this very reason than convergent series are axiomatically defined to have values (in other words, the Mathematicians writing the rules say "convergent series good") But when you take an infinite series of 0's written as alternating positive and negative ones, 1-1+1-1+1-1+.... (notated as Σ(-1)^n), the series diverges. [The notation means the n-th term in the series is (-1)^n. So if n is even, the term is 1, and if n is odd the term is -1; the "0th" term is 1, then the 1st term is -1, then the 2nd is 1 again, and so on they alternate back and forth] Taken one by one you get 1, then 1-1= 0, then 1-1+1= 1, then with the next term added 0 again, then 1 again, then 0, then 1, on and on. You can see here the series does not converge to single value, but bounces back and forth between 1 and 0. This can cause a lot of problems in continuity, as this video shows, so it (along with all other divergent series) are axiomatically defined to be undetermined or have no value (Mathematicians writing rules say "divergent series bad"; very similar to why in math we say you can't divide by zero. Why? because it just messes everything up, that's why). [Tangent: Keep in mind this is all within the context of the field of Real Analysis. There are other fields of math where divergent series are assigned values (and problems in continuity are solve in other, more complicated ways). In the context of Cesaro Summation, the series 1-1+1-1+1-1+..., which bounces back and forth between 1 and 0, would be defined to equal 0.5 or 1/2.] So where is the "error" in this proof? Well remember we said 0+0+0+0+... is notated as Σ0. This means that 0 is the individual terms being added [0 is the 0th term, and the 1st term, and the 2nd, etc.]. This is fine. In the next step he writes (1-1)+(1-1)+(1-1)+.... This is ambiguous, but could reasonably be notated as Σ(1-1). Here he is writing the same series Σ0, but writing the 0's as (1-1). If you take each (1-1) to be an individual term [(1-1) is the 0th term, and the 1st term, and 2nd, etc.], this is still technically fine. It's an awkward way of writing the series (and not at all the way you should necessarily do it), but still works assuming you only consider the +1's and -1's in chunks that cancel each other out. In the next step, though, he separates the first 1 from all the other terms and rearranges the parentheses to be 1+(-1+1)+(-1+1)+(-1+1)+... This can obviously only be done if each +1 and -1 is considered a separate term [1 is the 0th term, -1 is the 1st term, 1 the 2nd, -1 the 3rd, etc]. Here the sequence would have to be thought of as Σ(-1)^n, where the (-1)^n are the individual terms. And this, as shown above diverges. So in two inconspicuous steps, he has subtly transitioned from a definitively convergent series, to a very ambiguous series, to a definitively divergent series. Furthermore he really just flat out changed the series from Σ0 to Σ(-1)^n, which despite looking similar are two very different series. That's the error. Finally he simplifies the 1+(-1+1)+(-1+1)+(-1+1)+.. to 1+0+0+0+... which can be thought of as 1 + (0+0+0+...) or 1 + Σ0. As since we defined Σ0 = 0, this equals 1. But of course we only defined Σ0 = 0 because it converges, and again the same trick is used. If the +1's and -1's are thought of as separate terms, the series obviously diverges. But if the (-1+1)'s can be simplified to (and therefore thought of as) individual terms equaling 0, then it converges. Here he has pulled a single 1 out and switched the Σ(-1)^n back to a Σ0. [Technically by pulling a 1 out the remaining series is Σ(-1)^(n+1), which is different (Cesaro sum is now -1/2), but same idea applies] So in conclusion, the trick of this proof is to take a convergent series (which in Real Analysis is considered valid), subtly transition it to a divergent series in order to take out a single 1 (invalid), and then quickly change it back to a valid convergent series before anyone notices what happened. It's like burglar picking your lock, stealing a single piece of jewelry, and relocking the door on the way out. You may never even know what hit ya!
Technically by the way he solved it, he did 1+0=1. Since the first zero is a positive, it must have its negative pair to equal zero. Through his solution, he never includes the negative one, thus getting him 1, which is obviously not correct. His Solution: 1+(-1+1)(-1+1)...=1 (There are only 5 1s, whereas there must be 6 to equal 0) Correct Solution: 1+(-1+1)(-1+1)-1...=0 0 ≠ 1
DrouxDrew The point is that there are an infinite number of -1s and 1s, since there are an infinite number of zeros. This means that the final solution you get depends on where you choose to cut off the sequence, so 0 = 0 = 1. The point of the lesson is to explain why you can’t use normal laws of rational numbers when dealing with infinity, otherwise you get paradoxical equations like this
@@nameless4753 there may be infinite -1 and 1 but they are in a pair not individual so you can't simply just include 1 or -1 without including the other
The proof is wrong 🤦♂️u wont be able to proove anything always remember when ever you are proving some dumbshit like this you are breaking the rules of mathematics somewhere or the other
For anyone who is confused, on the second equation he removed a -1. You can see this because if you count the total number of +1’s and -1’s in the first equation, it would be 5 of each which is 10 total. In the second equation, it’s 5 total +1’s and 4 total -1’s meaning he is missing a -1 in the equation. So it will always be 1+0+0+0+0+(-1) plus an infinite amount of zeros, not 1+ an infinite amount of zeros. Meaning that the next integer is negative one, before subtracting 1 from negative one an infinite number of times. 0=1+…[-1+(1-1)*infinity]. Which simplified would be, 0=1+…[-1+(0*infinity)]. Even further simplified it would be, 0=1+…[-1+(0)]. Again, 0=1+…-1 and eventually, 0=0. Not the ellipses represent the quantity (-1+1) summed “n” number of times which would just be zero summed “n” times which is just zero.
There is something messed up in the third line, as you written "0=(-1+1)" but then you splitted the components of the bracket and taken +1 in the first but (-1) must need to added at last.
I think he was about to explain the issue after saying 0 = 1, but the video was cut short, so we'll never know. This is my take on it anyway: An infinite sum is equal to limit of the sequence of its partial sums (when the limit exists). So [A] 0 + 0 + 0 + 0 + 0 +... Gives the sequence 0, 0, 0, 0, 0, 0, ... which has limit 0. And [B] (1 - 1) + (1 - 1) + (1 - 1).... Gives the sequence 0, 0, 0, 0, 0, 0, ... which has limit 0. (same as previous sequence) And [C] 1 - 1 + 1 - 1 + 1 - 1.... Gives the sequence 1, 0, 1, 0, 1, 0, ... which has no limit. And [D] 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) +.. Gives the sequence 1, 1, 1, 1, 1, 1, ... which has limit 1. And [E] 1 + 0 + 0 + 0 +.. Gives the sequence 1, 1, 1, 1, 1, 1, ... which has limit 1. (same as previous sequence) So therefore you cannot just jump from B to C (they have different limits) by removing the brackets. Intuitively it feels like you can, but that intuition is just borrowed from summing finitely many terms, in which there would be no problem. Also jumping from C to D is wrong (they have different limits), you cannot just add brackets in. Similarly to above it feels intuitively correct, but its not. So in summary, there would be 2 errors in his proof, the first is when he removes the brackets, the second is where he adds them again. Hope that helps explain it.
A (finite) limit of an infinite series exists iff you can approach a fixed value as 'close' as you wish by summing a sufficient amount of terms, i.e. iff for any error value 'e' you can always pick some 'n' such that for any N > n, summing the first N terms gives a value that is less than 'e' distance from some fixed value 'r' -- the limit.
cream bun Infinite limits are extremely common in calculus and are very important to math. A function has a limit if it approches something. IE lim as x->inf of 1/x equals 0. A series has a limit if it converges on a value. In more advanced math there are ways of quantifying the values of infinite sums such as 1+2+3+4+5+...=-1/12. Although these are not truly equal in the traditional sense.
Gareth Reynolds the only thing about your comment is that in order for a series to converge, its sequence must converge to 0. 1/x is the harmonic series, so yes the sequence converges to 0, but the series diverges (grows endlessly forever). This is the exception to the lim as x -> inf rule. Any other series that passes the nth term test and others that prove convergence would be a series that converges.
cream bun, Colin Java is discussing a mathematical limit not a limit in a way where the numbers would stop. In math, the limit is what a function, sequence, or series's y value appears to become as x approaches some value. So in the first sequence, where every term is zero, the limit would be zero because no matter how many x terms you have, the y value will also stay zero. In the case of Colin's sequence C, the y values alternate between 1 and 0. Since the value will always bounce back and forth, there is no limit as y can never approach just one of them. Hope this helps.
I have my own 0=1 proof. By euler's identity e^it=1 Take natural log of both sides. ln(e^it)=it ln(1)=0 So, it=0 And as a formality, divide both sides by it it/it=1 0/it=0 So 1=0
@@Fotelek01 ahh you dont understand lemme show you In order to have 0=0 we have to equal substance 1 from 1,like this:0=1-1+1-1+1-1+1-1 so we have 0+0+0+0 But the teacher said 0=1+(1-1)+(1-1)+(1-1)....... and he forgot about a final -1 in the end
Hey I just thought of another way to proof 0=1 while watching this. The proof goes: 0 = 0+0+0+0+0+... (an infinite number of zeroes added together) Hence there are an infinite number of zeroes added together we can rewrite our equation as: 0 = ∞ • 0 Now we can use limits to evaluate ∞ • 0 lim (x • 1/x) x->∞ As x approaches infinity, x becomes infinity and 1/x becomes 0 Now we also realize that the x cancel out and the final limit we get is: lim 1 x->∞ There is no x to approach infinity, hence the answer is 1. Thus, 0=1.
For the equation to equal zero, the ones must come in pairs as it does not converge, it is actually periodic. So you cant isolate just the first one, you have to have another minus one to pair with it and complete period or cycle or whatever you call it. Otherwise you would be able to group all the positive ones you wish and repeat the infinite series afterwards and claim it equals any value you want
Well that’s the thing about infinite sums, if you rearrange them then yes you can make it equal whatever you want. But that’s not a problem with math or anything that’s something that is well understood so he is allowed to say that the first sum equals zero and the second sum equals one but since he rearranged the infinite sum he cannot say those two sums are equal, which he knows.
@@nathanielroosevelt1489 infinite means here (1-1) is being repeated infinite times not( -1 +1), if first number is 1 last number should be -1, so that it satisfies 0+0+0+0....... He just ignored the initial statement that is 0+0+0+...... and added an extra 1 at the beginning.
@@mr.noname6109 he did not add an extra 1 it’s just that, like you said, (1-1) is being repeated not (-1+1) so even though the notation is the same the sum is not because of the grouping and that’s all I was saying.
@@nathanielroosevelt1489(1-1) or (-1+1) is no different in group or sum. They all have pairs and you can't rearrange that and pretend infinity cancels out your rearrangement, that's all it is.
Not only one chance but many chances. Because 0=0+0+0+...... and we can prove each individual 0 as 1 by above process. So then 0=anything. Or we can write 0=(2-2)+(2-2)+(2-2)+..... In this way also we can prove 0=anything. So you have any number of chances with your crush. Don't worry hero.
@John Hush Sir, im a student and i havent any idea about calculus or others. But i think the error is in the first step . 0 = 0+0+0+0+0+……… Its equal to 0(1+1+1+1+1+……) 👆👆👆 This equal to infinity. That is, you have multiplied something by infinity. It is undefined. Thats why we finally got 1. Please can you explain this.
Let's start by considering the series 0 + 0 + 0 + ..., which is an infinite sum of zeros. We can represent this sum with the mathematical expression: S1 = 0 + 0 + 0 + ... Now let's consider the series (1-1) + (1-1) + (1-1) + ..., which is an infinite sum of pairs of numbers that are respectively 1 and -1. We can also represent this sum with the mathematical expression: S2 = (1-1) + (1-1) + (1-1) + ... Note that each term in S2 is equal to 0, since 1-1 = 0. Therefore, we can simplify the expression for S2 to: S2 = 0 + 0 + 0 + ... We can see that S1 and S2 both represent the same divergent series, and both can be described by the expression 0 + 0 + 0 + ..., but that doesn't mean that they are equal to each other or to any other number. Even though it may be tempting to take the expression (1-1) + (1-1) + (1-1) + ... and say that it's the same as 1 + (-1+1) + (-1+1) + ..., it's actually not correct to do so. When we distribute the parentheses in the last expression, we change the order of addition and create new terms in the series. Therefore, it's not correct to simplify the expression in that way. The conclusion is that even though it may be tempting to use algebra to manipulate divergent series, it's important to remember that they don't obey the same rules as convergent series, and that you should be careful about taking expressions out of context.
User 0= 1 ? ChatGPT The expression "0 = 1" is a mathematical statement indicating equality between two values, where "0" is on the left side and "1" is on the right side. However, this statement is false because 0 does not equal 1. In mathematics, the equals sign (=) is used to denote that the expressions on both sides have the same value. So, "0 = 1" is not correct in any mathematical context. User Prove that: 0=1 ChatGPT Actually, proving that 0 equals 1 is not possible because it's fundamentally untrue in mathematics. In mathematics, equality means that two expressions represent the same value. However, 0 and 1 are distinct numerical values, and there's no mathematical operation or reasoning that can make them equal. If you're interested in exploring the topic further or if you have a specific context where you'd like to discuss something related, feel free to share!
I'm afraid you've misunderstood at calculation Mr. Hush 1:05 Here's the thing, the (1-1) thing is infinite so you can't just say that 1+(-1+1)+(-1+1)+... equals to 1+0. You know, you can't define the last number. Even if you will say that it can be defined like 0= (1-1)+(1-1)+(1-1)+(1-1) in the end you will still get 1+(-1+1)+(-1+1)+(-1+1)-1 and is still 0=0
@Amarok alright ima explain this as easy as possible. Lets say that you can define the last bracket in this infinity. Its going to be 0 = (1-1)+(1-1)+...+(1-1) and you moved the brackets so its gonna be 0 = 1+(-1+1)+(-1+1)+...+(-1+1)+(-1) which can also be said as 0 = 1+0+0+0+0+...+0+0+0+0+(-1) You know. It comes in pair of (-1+1) so the 1+0+0+0+0+... = 1 is impossible. like if there's 1 infront. then there's -1 at the back
I agree you however, it is not that you cannot know the last number but that there is no last number because these infinite series are in ordinal space not cardinal.
Actually, I spotted one mistake. Because he is shifting the bracket to the next, he is borrowing the +1 from the next zero. Which leaves a -1 from the last zero. But he forgot to write it down. If he takes a fixed number of zeros, it will clearly show this error. 0 = 0 + 0 + 0 + 0 0 = (1-1) + (1-1) +(1-1) + (1-1) What done wrong during shifting is he forgot to write the last -1 0 = 1 + (-1+1) + (-1+1) + (-1+1) + (-1) 0 = 1 + (0) + (0) + (0) + (-1) 0 = 1 + (-1) 0 = 0 There are lots of interesting mathematics in this world... I do appreciate his efforts, because only when people things outside of the box.... New inventions get born. So I do appreciate his work & inspiration :)
Me: “Hey can you give me 0 dollars?” Friend “Sure??” Me: “You gave nothing.” Friend: “Yes I know that’s the point right? Me: “Let me show you something...”
This proof is not correct If your maths is good then you can understand it in 3rd step (Last line at bottom of board) in which he is making pairs of -1+1 and at last he miss -1 His pairing is not correct
Fractional defines the possible variations of the element grouping in one gruop of elements, when there are zero elements in a group you can only group them in one way, im not good at professional math language, so it might be a little bit different from the reality
For the math experts in the comments: there is no “last” -1, the series is infinite. The problem is his reasoning only applies to convergent series: the one he used is not among them.
@@alisalimli tit is not infinite positive one) plus (infinite Negative ones) becouse you can not know if there are the same Numbers of positive and negative ones. I mean, if we go to the third term (or any odd term of the serie) , we will obtain 1+(-1)+1= 1, but if we go to te fourth term ( or any even term) we will have 1+(-1)+1+(-1)=0 Infinite is not even neither odd cause infinite is not a number, just a mathematic concept so the second serie does not converge to any number so it is not equal to the first one. The first one you know that it converges to 0 but the second does not converge.
@@edudavila8475 Bro, what you said makes no sense…. There needs to be a -1 at the end of 1+(1-1)+(1-1)… -1, this would be correct. The way he did it was by using a equal sign where you can’t use one because what he did messed with the term…. It does not have to do anything with infinite being odd or not. You substitute a 0 with 1-1, if you multiple that with any natural number (you need to use the natural numbers or else it messes with the term, you can’t use the rational numbers), this will never result in an odd number of 1nes. Meaning what you said in the comment is wrong…
@@zhangkevin6748 What do you mean with second series i don’t understand what you mean with that. I corrected Edu d‘Avile because he is wrong. What he said was wrong. He said we don’t know how many 1 and -1 there are, but we know it. At least we know there has to be the same number of them. The 1+(-1)+1=1 can’t exist, or can you explain how there are 2 times 1 and 1 time -1… you can’t. Even just saying 0=1 is wrong, it’s plain wrong mathematically. We both know that if you take something wrong you can prove whatever you want with it, it doesn’t matter. It then can be true or false we don’t know.
infinity is fine, the problem is when you rewrite (1-1)+(1-1)+... as a summation, you get sigma( (-1)^n ) so really what you don't wanna mess with is a negative number raised to a variable. try graphing this.
At 1:25, there is supposed to be a -1 (at the end of the series. Which even though doesn't seem to end, but when the sum of the zeros is done is done, it will appear) which would cancel the first 1 and would result in 0.
myths destroyer lol i knew you were not that stupid i was just playing around in your play if you were that stupid then you probably wont be able to write comments
John Hush but won’t there always be a left over - 1. You’re talking about infinite. But even with these rules you will always have a minus one that will be pared up with the plus 1 at the beginning. Like a circle, no end no beginning, it just goes back to where you start. I would still think this is correct
@@lorenzolevi5402 it doesn't make sense to talk about something left over in an infinite series; there's no end to it so there's never anything left over
@@mrjohnhush You grouping 10s of (1-1) but in the grouping there is an unpaired 1, it means that if I want to go back one step before the grouping, I will not get to it unless I draw back one 1 from the... 1
@@sisaxazana309 the problem is you can't claim that there will be an extra - 1 For example you can't find the largest positive number There might be an extra - 1, there might not be That's the actual answer that we don't know what happens at infinity Infact we don't even know if adding infinite number of 0s will give 0 or not
For those who couldn't understand... In the 2nd line, you can see there are ten number of 1. But while writing the 3rd line, he has started the expression with +1 ended it with +1 and the number of 1 counts upto 9, that is he has not fulfilled the expression with the previous one. So he reminded with +1 at last.. The main trick here is that, the more the number of 1 you are writing, the more trickier gets the equation and easy is to fool others
My maths teacher showed this to us in high school too. I always really likes this proof because it so neatly diverts attention to the wrong place. It seems so obvious that shenanigans are going on when you move the brackets that people completely forget to think about the casual and seemingly logical assertion that 1-1+1-1+1-1... = 0.
My maths teacher showed this to us in high school too. I always really likes this proof because it so neatly diverts attention to the wrong place. It seems so obvious that shenanigans are going on when you move the brackets that people completely forget to think about the casual and seemingly logical assertion that 1-1+1-1+1-1... = 0.
@@trixieofthetrade7494I think the wrong portion is how he grouped it. (1-1) + (1-1) turns into (-1-1)(-1+1) which effectively produces 0. How he got that, I have no idea, but it is completely wrong since x + (x-x) = x so in any local sense this form of grouping is wrong.
I got here after watching Modern Family's S10E21 haha I think the problem here is the use of an infinite series to prove 1 = 0 When you say 1 = 0 + 0 + 0 +... and then 1 = 1 - 1 + 1 - 1 + 1 - 1... you end up with Grandi's series Σ(-1)^n which is a divergent series and has no sum, at least in the usual sense. Love your videos John!
Actually it's more the fact that the structure of divergent series is not a group (endowed with addition) means that you literally can't manipulate divergent series with + or - (btw i'm not a native english speaker it may be the wrong mathematics name)
Don't know whether this is correct or not but that's a Geometric progression right there: 1,-1, 1,-1.... And the sum of a GP is given by a(1-r^n)/(1-r), where a is the first term and r is the common ratio. So, here, a=1, r=-1 If we take n to be an even number we get, 1(1- (-1)^even number)/(1-(-1))=0. But if we take n as an odd number, we get 1(1-(-1)^odd number)/(1-(-1))=1. It all depends on how many terms we are considering in the series.
It is wrong because the lecturer had used the brackets incorrectly when transitioning from (1-1) + (1-1)+(1-1)+.... and then saying that 1+ (-1+1)+(-1+1)... We clearly see the change of the use of brackets changes the nature of the sum. Meaning (1-1)+(1-1)... Is not equal to 1+(-1+1)+(-1+1). Additionally, we see the reason that the second sum is equal to 1 is because it has an extra term like my previous example (1-1)+(1-1) has four numbers whereas 1+(-1+1)+(-1+1) has 5 numbers. I hope this makes sense
1 = 1 + inf*0 Does NOT equate to 1 = 1 + inf*(-1+1) -1 = 1-1 = 0 Changing the repeater is flawed. That's like saying the sum of infinite whole pizzas, without cutting any, results in a bunch of whole pizzas and a half of one. The only way you'd get that half is by cutting a pizza, and that's exactly what he did.
You can disprove this since every 0 = 1-1, but when he takes out that "1", he is going to have to take out "-1" at the end of the infinite sequence. This would give 1 + (-1+1) + (-1+1) + ....-1, which equals zero.
yeah if you go on mathologers video they explain properties of infinite series and how changing parentheses in one completely changes the meaning, that’s how people screwed up with the 1+2+3+4... = -1/12
@@commie281 A=1-1+1-1+1-1... 1-A=1-(1-1+1-1...) 1-A=1-1+1-1+1-1... 1-A=A 1=2A 1/2=A (I don't have enough skill in English to explain that, hope you will understand)
First of all, Infinity is not considered to be a number And second, dividing a number with itself doesn't give you 0, it gives you one, so if infinity was a number, dividing with it would give you: 1 + 1/infinity = 1
Bank : $0
Me : 1000000+(1000000-1000000)+(1000000-1000000)...
ooof, best comment of 2019
Hey... stop cheating
That goes for -1000000$ too bruh.
Oh yeah, it's big brain time.
You're a legend
Me: "Teacher, how many questions did i get right?"
Teacher: "0"
Me: "Let me show you something"
😂
LMAO
Hahhaahaa
🤣🤣
0 IS 0!
Teacher: "the test isn't hard"
The test:
Jesus 😆😂 funny
That was easy to get whats wrong?
@@kaitheemo Easy to get but not easy to cross your mind as an answer to a question when youre under time pressure while writing a test or exams
The test : proof that 0 equals 1
the test: prove that 1=0
I love that depending on how you define the result of an infinite sequence, you can "proof" 0=1, 1=2, -Inf = +Inf and so on.
It's the magic and horror of working with infinity.
👌✌️
@John Hush
Yes
Its not done right
@@bruvance Idc, it's funny.
Also that the sum of all natural numbers is actually 0 :)
He had a video that was 2=1
Does that mean:
0=1
0=2
1=2
Give this man an award...
Keira Wright no
Well, if you know that 0=1, you can prove that every number equals every number
Markone Fotbal 10 = 4
That means the whole world, humanity, nature, the universe is equal to each other.
You can't apply the commutative and associative laws to infinite series.
Thats why infinity times zero is actually not equal to zero
Good points. You understand what's going on here but most people are stumped. Please see if you can fool many others by sharing and promoting this video. Thanks a lot.
Math = Indian ?
Don`t argue with an Indian about maths. They`ve done their homework.
Wait does that mean if i added a bunch of infinite nothing or zeros I will get more than a zero nothing by adding a bunch of nothing
@@user-vu4hr4fk3t infinity isn't a "bunch", you can't represent it as just a number
This man is still liking comments after 8 years! What a legend
Agreed😂
Legend indeed
Do't be happy he is not like ur cmmt yet😀
Hagah, you copy that comment and don't get 50.000 likes😂😂
except ya...
Sir to take out 1 out of the 1st bracket it is essential to also subtract 1 otherwise it is impossible to take out 1 out of the 1st bracket and do grouping. Therefore without subtracting 1 when grouping makes your 3rd step invalid. By virtue of taking out one and grouping you are subtracting one automatically . So you cannot have a one standing alone +sum of infinite 0s. You are obliged to subtract 1 immediately you start doing the grouping.
i.e (1-1)+(1-1) = 1+(-1+1)-1
You must immediately subtract 1 when you take out 1 out of the first bracket and start grouping.
I was just thinking that...PEMDAS more or less destroys his proof. Probably more accurate to say the sum of series is zero _or_ one if that first 1 isn't grouped.
Let's take a moment and appreciate him that he is still replying to comments and liking them even after 8 years
Well it’s awkward how he didn’t reply or like this comment.
@@currymuncher5958 I didn't said that he is replying to every single comment.
Why
Maths
Albert polynomial
ruclips.net/video/1dhTGpc0mHQ/видео.html
One time must see...
But not to your comment lol
So turns out that I've been a billionaire my entire life.
Ah, Perry the platypus, i will now unveil to you my Coronovirus-inator!
*TUM TUM TUUUUUM*
Maths
Albert polynomial
ruclips.net/video/1dhTGpc0mHQ/видео.html
One time must see...
Where are you Perry
@@vectr1310 he in my trap
If you proof like that. 0 equals all numbers.
Chill Down. It was a joke
!!!!
@Creeper Gaming eder bebeğim ben ettiriyorum.
@@sdwvxic-1711 infinity isn't number you can multiply. And if it were possible infinity * 0 + 1 would be equal to 1 because anything times 0 is equal to 0. Thus adding 1 would make it 1.
@@KiemPlant actually if i remember well if you have a serie that limit is 0 and another than goes to infinity and multiply them, the resultant serie can go to anything and you have to do more calculation to find its true limit
(sry i don't know english maths terms very well)
0 x infinity can be any number in this case, so we say it is not defind
yes
I don't hate math but my teachers in high school made me hate it. Students who are bad at math were scared to ask questions from them because they always scolded us for being slow learners in math and embarrass us in front of the class forcing us to solve problems on board, even though we were trying our best to understand.
Having a teacher like you, makes me want to say that learning math is fun! ☺️ And you explained it in a way that it isn't hard to understand. Thank you!
search "eddie woo" on youtube, he is practically the best math teacher on the planet. He's got everything from basic math to advanced calculus. I currently take AP Calculus AB and im literally the top student just bc of him. He is amazing, He's also done a ted talk as well; he is worth checking out.
maybe its not the teachers fault, when algebra and calculus is introduced, only the real math enjoyers are left to enjoy math
THIS, I learn at a convent jr.college here in India and this is the same problem with me, I wish there was a better teacher who wouldn't embarass you in front of the whole class for asking some basic doubts
“Okay one more proof.”
Last online 8 years ago.
Haha! There are other more recent ones on my channel. And that's no spoof! 😜
@@mrjohnhush you're answering to videos which are 8 YEARS old...wooow respect man
Wowowoowowow
@@mrjohnhush are you still teaching in school? (apart from the corona thing I mean)
@@marcellehner4156 No, I've been retired 3 years. I tutor and make more videos though.
They nerfed this in the last 3.4 patch notes. Sorry guys it doesn’t work anymore. 😪
Sean Bautista fuck man
explain please, I dont get it
@@mirage_panzer2274 maybe next life
Der PanzerFauz he’s talking about the fortnite update in 2018
Seb Beast this isn’t a fortnite joke, it’s a gaming joke. Fortnite’s obviously the only game you’ve ever played.
My teacher: You have 1 assignment to do today
Me: *thats where you're wrong, buckaroo*
all fun and games till they hit you with the 1=2
@@ediblenebulas1164 and you strike back with a 2=0
@@Emanu3l LEGENDARY
@@ediblenebulas1164 they strike back with a 0=30, you strike back with a 30= -30they have to do the work.
@@Shadow-hz8ko BOOM ROLE REVERSAL
What a great video!
Let us take a moment to appreciate his efforts!
You are a great teacher!
Thanks! Please🙏continue to watch, share and promote my videos and channel with as many people as you can. It's greatly appreciated. 👍🥰✌️😇👌
@@mrjohnhush sure!🙏sir
Wait, if 0 = 1, then all those zeroes he wrote are also equal to one.
I hate myself
And you take this just over 2 and u got 0 you got 1 and you pass the test lol jk
TO PROVE 0=1
PROOF:- LET 0= x-1
Acc. To Question, x-1=1
x=1+1, x=2
Where, x-1=0
And We Finded x-1=1
And, x-1-0=0-----------eq(1)
x-1-1=0---------eq(2)
Divide Eq. 1 and 2
x-1-0 upon(by) x-1-1 it will be -0 upon -1 then -1 is in divide form Take It to the RHS and It Will be +ve...Hence Proved 0=1
so 0=1=∞
IconX Genius
Oh shit
0 o'clock: I have to go to sleep now
Me at 3am: proof that 0 equals 1
You can sleep at 1AM now
Lmaooo
This is exactly me at 3am rn LOL
Let me show you how 0 o'clock is actually 1 o'clock
5:30am** ://
So basically you can do this with every number, not only 1. That means, 0 is everything, and everything is nothing.
You missed the trick
@@tusharkumarraj6066 I didn't say that this guy is right. He isn't. I just wrote an interesting statement if it was real.
@@Dante-lh6nk he isn't right or wrong
It's a paradox
@@tusharkumarraj6066, In my opinion, he is wrong. He just didn't write "-1" which has to be in the equation but it can be so far away that he can never write it.
@@Dante-lh6nk nope , there are infinitely many (-1) and if you remove one -1 from infinity , it still remains infinite
hate to be that guy, but I can disprove this - i'm not sure if this is what the guy who objected near the end said, but this is how I do it:
in the second step, each bracket ends in a -1. this series goes on infinitely, so the theoretical 'last term' would be -1.
so in the third step, after all of the brackets of (-1 + 1), there has to be a -1 at the end, because the series cannot 'end' in a +1, it 'ends' in a -1.
so the +1 at the start and the -1 at the end will cancel out, totalling 0. this added to all of the other brackets still gives 0.
again, hate to be that guy, but it had to be said.
Judge: your are jailed for 40 years
Him: let me show you how 40=0
@Adolf Hitler no that 0=0
Judge: 0=1
@@R1ghtlysleepy69 1=2
@@afriendlycampfire260 2=3
3= i love you
*Mom* : Why did you get 0 on your test?
*Me* : My marks are beyond your understanding
FINALLY a slightly different joke!
Good.
😂😂😂😂😂😂
Ro the method he told is wrong so you wont be able to proove that
@Kian Saliany LOL but they are only good if they can find out where mistake is instead of that annoying kid in the class who doesn't know a shit but just wants to proove the teacher wrong
Me: Hey dad, can you give me 0 dollars?
Dad: Sure why not?
Me: Thanks, so give me 2 dollars.
Dad: Why? It should be 0.
Me: 0 is equal to one and one is equal to 2!!!!!
You've learned your lessons well! Did dad fall for it? 😂 Please watch, share and promote my videos and my channel. 🙏💙😎✌💓🎓 Many thanks. 💞
So if 0=1 and 1=2 so we can conclude that 0=2
@@troll_411 Absolutely! 😎🎓✌
@@mrjohnhush Can I Get A Reply Sir... ....🥺🥺
@@unknown.9177 Of course! If I see it I almost always respond. 💞✌😎🎓💙🙏🤗
Yeah, this is why calculus is always so specific about limits; if it were to say “infinitely small”, everything just breaks. Infinity is necessary, yet also the breaking point of all things maths
See you all in "2023 recommendation"
Hi future me
Let's see
*Hello future , we’re here talking to you from the first year of quarantine*
@@Youba05 yes yes we are
@@geraltdirivia8278 hahahaha
The very last -1 “am I a joke to your”
Yes a little bit stupid this explication. He did better
In infinity there is no end, so no last exists doesn't matter how far
@@retweaksatapathy106 still just a stupid approximation , doesnt work In real life
Tryan Frigor we’ll not shit Sherlock we all thought 0 did equal 1😂
"funny bone"
So you're saying if a guy had 0 dollars, he would have 1 dollar. 🤔Thanks that makes me 1 dollar richer... ;)
Wait...
What if I make a bunch of bank accounts with 0 dollars in each. Thanks John Hush for the idea. ;)
but if 0=1 & 1=2 & 2=5 as he has proven, that means youll make 5 dollars, and if you divide this 5 dollars to 5 one dollars then youll have 5 5 dollars, and so on, then youll have infinite money
Wtf😂😂
You must have bank account with 1 dollar and -1 dollar, so you can have 1 dollar. Actually you can
Or you could use any other number for your proof, for example 50 million. You could do 50mill +(-50mill+50mill)...
😂
I think we could've just simply proved it from 1^0=1^1. As the result of both sides is same i.e. 1 we can the powers are equal as well. Hence 0=1
Bro that’s like saying 1^5 = 1^99 so 5 = 99
@@VarunDoesMaths yeah it doesnt make sense right ? just like the video
This guy seems smart enough to know that 0 doesn’t equal 1
thanks!
Yes he does
This is why students are so stupid in this country😂
Of course he is xd, he just mofing with the students :v
@@lahermanadedalasesputa2933 dude fcking stop with the damn pacmans ffs
What i learned -
Dont mess with infinity.
Yeah.. 😂 same here
what u learned
u are an idiot ?
Nice pfp
Or this is pretty stupid. Math is math. Result is 1. This guy complicating does mean nothing. Result is 1
Set infinity equal to 1. Then infinity=0=1.
I think this is how black holes work
They don't work, they fixed it in the latest patch
Black hole are not infinite
Jesus Gonzalez so this big ball of nothing has an end?
M M I find it very troubling when contemplating that life could be a video game. It also makes me question my sanity
@@araxietyne Then don't
Not me being late 9 years. And this video just popping out in my recommendations. Having you as a teacher would be a blessing for everyone. By far the best teacher!!
Lot's of good thinking in the comments. But I have yet to find the mathematically "correct" explanation. So here's my very long and detailed attempt at explaining the official mathematical reason this proof is invalid. Hope y'all enjoy.
The first little complexity comes up in the first step where he says 0 = 0+0+0+0+...
Depending on the field of math, this can be right or wrong.
An infinite number of zero's is not necessarily 0, it's undefined until given further context.
Just as how 0 * infinity is considered undefined, 0+0+0+... and infinite number of times is also considered undefined without further context.
Now within the context of series (Real Analysis) he's right. The infinite series of 0's is axiomatically defined as 0 (meaning when Mathematicians write the "rules" of series, they make it true by rule that an infinite series of zeros is zero).
This is done for some obvious reasons. Otherwise any series could be made undefined just by adding a bunch of zeroes.
More precisely, and most importantly, an infinite series of 0's when writed 0+0+0+0+... (notated as "Σ0") is convergent. This means as you add more and more terms, the sum converges to one value, zero.
i.e. If you take each term one by one, you get 0, then 0+0= 0, then 0+0+0= 0, then with the next term added 0 again, and again, on and on. You always get zero, so it makes sense the series as a whole should be defined as 0.
It is for this very reason than convergent series are axiomatically defined to have values (in other words, the Mathematicians writing the rules say "convergent series good")
But when you take an infinite series of 0's written as alternating positive and negative ones, 1-1+1-1+1-1+.... (notated as Σ(-1)^n), the series diverges.
[The notation means the n-th term in the series is (-1)^n. So if n is even, the term is 1, and if n is odd the term is -1; the "0th" term is 1, then the 1st term is -1, then the 2nd is 1 again, and so on they alternate back and forth]
Taken one by one you get 1, then 1-1= 0, then 1-1+1= 1, then with the next term added 0 again, then 1 again, then 0, then 1, on and on. You can see here the series does not converge to single value, but bounces back and forth between 1 and 0.
This can cause a lot of problems in continuity, as this video shows, so it (along with all other divergent series) are axiomatically defined to be undetermined or have no value (Mathematicians writing rules say "divergent series bad"; very similar to why in math we say you can't divide by zero. Why? because it just messes everything up, that's why).
[Tangent: Keep in mind this is all within the context of the field of Real Analysis. There are other fields of math where divergent series are assigned values (and problems in continuity are solve in other, more complicated ways). In the context of Cesaro Summation, the series 1-1+1-1+1-1+..., which bounces back and forth between 1 and 0, would be defined to equal 0.5 or 1/2.]
So where is the "error" in this proof? Well remember we said 0+0+0+0+... is notated as Σ0. This means that 0 is the individual terms being added [0 is the 0th term, and the 1st term, and the 2nd, etc.]. This is fine.
In the next step he writes (1-1)+(1-1)+(1-1)+.... This is ambiguous, but could reasonably be notated as Σ(1-1). Here he is writing the same series Σ0, but writing the 0's as (1-1).
If you take each (1-1) to be an individual term [(1-1) is the 0th term, and the 1st term, and 2nd, etc.], this is still technically fine. It's an awkward way of writing the series (and not at all the way you should necessarily do it), but still works assuming you only consider the +1's and -1's in chunks that cancel each other out.
In the next step, though, he separates the first 1 from all the other terms and rearranges the parentheses to be 1+(-1+1)+(-1+1)+(-1+1)+... This can obviously only be done if each +1 and -1 is considered a separate term [1 is the 0th term, -1 is the 1st term, 1 the 2nd, -1 the 3rd, etc]. Here the sequence would have to be thought of as Σ(-1)^n, where the (-1)^n are the individual terms. And this, as shown above diverges.
So in two inconspicuous steps, he has subtly transitioned from a definitively convergent series, to a very ambiguous series, to a definitively divergent series.
Furthermore he really just flat out changed the series from Σ0 to Σ(-1)^n, which despite looking similar are two very different series. That's the error.
Finally he simplifies the 1+(-1+1)+(-1+1)+(-1+1)+.. to 1+0+0+0+... which can be thought of as 1 + (0+0+0+...) or 1 + Σ0. As since we defined Σ0 = 0, this equals 1.
But of course we only defined Σ0 = 0 because it converges, and again the same trick is used.
If the +1's and -1's are thought of as separate terms, the series obviously diverges. But if the (-1+1)'s can be simplified to (and therefore thought of as) individual terms equaling 0, then it converges.
Here he has pulled a single 1 out and switched the Σ(-1)^n back to a Σ0.
[Technically by pulling a 1 out the remaining series is Σ(-1)^(n+1), which is different (Cesaro sum is now -1/2), but same idea applies]
So in conclusion, the trick of this proof is to take a convergent series (which in Real Analysis is considered valid), subtly transition it to a divergent series in order to take out a single 1 (invalid), and then quickly change it back to a valid convergent series before anyone notices what happened.
It's like burglar picking your lock, stealing a single piece of jewelry, and relocking the door on the way out. You may never even know what hit ya!
How long did it take you to write that!?
@@magicac3138 Probably like an hour or two.
I- what? My brain is too smooth for this-
wtf holy jesus moly what the hell? What are you?
@@mrcheese1373 Just a big math nerd
Technically by the way he solved it, he did 1+0=1. Since the first zero is a positive, it must have its negative pair to equal zero. Through his solution, he never includes the negative one, thus getting him 1, which is obviously not correct.
His Solution: 1+(-1+1)(-1+1)...=1
(There are only 5 1s, whereas there must be 6 to equal 0)
Correct Solution: 1+(-1+1)(-1+1)-1...=0
0 ≠ 1
DrouxDrew The point is that there are an infinite number of -1s and 1s, since there are an infinite number of zeros. This means that the final solution you get depends on where you choose to cut off the sequence, so 0 = 0 = 1. The point of the lesson is to explain why you can’t use normal laws of rational numbers when dealing with infinity, otherwise you get paradoxical equations like this
In your comment you set the problem to a definite amount while in his video he sets to an infinite amount
DrouxDrew you did not receive a like from John Hush
@@nameless4753 there may be infinite -1 and 1 but they are in a pair not individual so you can't simply just include 1 or -1 without including the other
Cha Ching! The price is right!!!!
Binary programmers are having heart attacks just by seeing the title of this video
LOL. Give them a decent burial. 😜
Sir,you are great
@@mrjohnhushIt seems that Mathematician are good at cracking jokes🤔
Your comment has 64 likes. That's going to make certain people who know binary quite happy. And maybe some minecrafters too.
I Made It 69 Likes Lol🤣
The man is still liking comments after 12 years...! What a legend.
People- why 9yrs old channel has 219k subs
Mr Hush- lemme show you how 219k= 2.19 million
Stolen comment
You copied someone else’s comment
Let me show you guys how this comment is the original and the other one is stolen.
@@Sw33tG4mer gold
The proof is wrong 🤦♂️u wont be able to proove anything always remember when ever you are proving some dumbshit like this you are breaking the rules of mathematics somewhere or the other
Teacher: you got zero at the test
Me: lemme show you how this zero equals to 💯
Edit- Holy shit 500+ likes damn
Lol
I think i should try this method when i test and get zero..
Captain Saom oh yeah yeah
@@yosuacalvin2331 are you joking rn? 😂
You have 666 likes lol
2012:
2013:
2014:
2015:
2016:
2017:
2018:
2019:now is the time
How original and creative!
Here for 2023 recommended section
Annoying
I hate youtube
2119*
For anyone who is confused, on the second equation he removed a -1. You can see this because if you count the total number of +1’s and -1’s in the first equation, it would be 5 of each which is 10 total. In the second equation, it’s 5 total +1’s and 4 total -1’s meaning he is missing a -1 in the equation. So it will always be 1+0+0+0+0+(-1) plus an infinite amount of zeros, not 1+ an infinite amount of zeros.
Meaning that the next integer is negative one, before subtracting 1 from negative one an infinite number of times. 0=1+…[-1+(1-1)*infinity]. Which simplified would be, 0=1+…[-1+(0*infinity)]. Even further simplified it would be, 0=1+…[-1+(0)]. Again, 0=1+…-1 and eventually, 0=0.
Not the ellipses represent the quantity (-1+1) summed “n” number of times which would just be zero summed “n” times which is just zero.
Moral of the story:
Never divide by zero
Never use infinity during math
Quick question, does infinity exist?
0=(1-1)+(1-1)+(1-1).........
If S(infinity)=a(1-r)^-1
S = 0(1÷(1-0))
Proof 0 = infinity
according to this every number in the world is = 0
How
Yes, it is so......🤕
@@azaralxandro2371 if 0=1, then 2=1+1=0+0=0
it also shows up that 0 is not equal 0..
No,no,no. That was proved by another guy,second name Sherlock first name No Shit.
Who is here after prove 2=1?😉😂
👇👇👇
0=1
1=2
soooooooo
0=2😃
@@hos5374 😂😂
@@mdintjar7987 2+2=0+0
4=0
@@hos5374 where are you from?
@@mdintjar7987 Syria🇸🇾🙂
There is something messed up in the third line, as you written "0=(-1+1)" but then you splitted the components of the bracket and taken +1 in the first but (-1) must need to added at last.
Yep.
"But i'm only 14"
"Let me show you something"
This is actually hilarious
Underrated comment 😂😂😂😂
Hol up
Wayment
Hahahaahh
I think he was about to explain the issue after saying 0 = 1, but the video was cut short, so we'll never know.
This is my take on it anyway:
An infinite sum is equal to limit of the sequence of its partial sums (when the limit exists).
So [A] 0 + 0 + 0 + 0 + 0 +...
Gives the sequence 0, 0, 0, 0, 0, 0, ... which has limit 0.
And [B] (1 - 1) + (1 - 1) + (1 - 1)....
Gives the sequence 0, 0, 0, 0, 0, 0, ... which has limit 0. (same as previous sequence)
And [C] 1 - 1 + 1 - 1 + 1 - 1....
Gives the sequence 1, 0, 1, 0, 1, 0, ... which has no limit.
And [D] 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) +..
Gives the sequence 1, 1, 1, 1, 1, 1, ... which has limit 1.
And [E] 1 + 0 + 0 + 0 +..
Gives the sequence 1, 1, 1, 1, 1, 1, ... which has limit 1. (same as previous sequence)
So therefore you cannot just jump from B to C (they have different limits) by removing the brackets. Intuitively it feels like you can, but that intuition is just borrowed from summing finitely many terms, in which there would be no problem.
Also jumping from C to D is wrong (they have different limits), you cannot just add brackets in. Similarly to above it feels intuitively correct, but its not.
So in summary, there would be 2 errors in his proof, the first is when he removes the brackets, the second is where he adds them again.
Hope that helps explain it.
If it is infinite how can it have any limit at all? That is what infinity means, no limit, so it voids itself by default.
A (finite) limit of an infinite series exists iff you can approach a fixed value as 'close' as you wish by summing a sufficient amount of terms, i.e. iff for any error value 'e' you can always pick some 'n' such that for any N > n, summing the first N terms gives a value that is less than 'e' distance from some fixed value 'r' -- the limit.
cream bun Infinite limits are extremely common in calculus and are very important to math. A function has a limit if it approches something. IE lim as x->inf of 1/x equals 0. A series has a limit if it converges on a value. In more advanced math there are ways of quantifying the values of infinite sums such as 1+2+3+4+5+...=-1/12. Although these are not truly equal in the traditional sense.
Gareth Reynolds the only thing about your comment is that in order for a series to converge, its sequence must converge to 0. 1/x is the harmonic series, so yes the sequence converges to 0, but the series diverges (grows endlessly forever). This is the exception to the lim as x -> inf rule. Any other series that passes the nth term test and others that prove convergence would be a series that converges.
cream bun, Colin Java is discussing a mathematical limit not a limit in a way where the numbers would stop. In math, the limit is what a function, sequence, or series's y value appears to become as x approaches some value. So in the first sequence, where every term is zero, the limit would be zero because no matter how many x terms you have, the y value will also stay zero. In the case of Colin's sequence C, the y values alternate between 1 and 0. Since the value will always bounce back and forth, there is no limit as y can never approach just one of them. Hope this helps.
I love that comment section is still active !!!!
Indeed! I try to keep an eye on it and respond. It's hard to keep up. 🎓😇✌💙
@@mrjohnhush are you actually the teacher or just a random student?
@@user-pe2xj5dr9r Yes, I'm the teacher! You'll probably realize it if you watch more of my videos. 😎✌️🇨🇦💙👌💫💜
@@mrjohnhush ah ok ill make sure to watch more
@@user-pe2xj5dr9r Thanks again! Please also share and promote all the ones you like. It's greatly appreciated. 💞
I have my own 0=1 proof.
By euler's identity
e^it=1
Take natural log of both sides.
ln(e^it)=it
ln(1)=0
So,
it=0
And as a formality, divide both sides by it
it/it=1
0/it=0
So 1=0
„The problem with infinity is, all sorts of weird things happen when you‘re dealing with infinity“
What if 420=69
aa kala 420=69=666
Erica L yeah thats the best answer
Erica L 420=69=666=1337
420+69+666+616=earthisflat
911 = bush
After three dots we have got one - 1
I mean:
1+(-1+1)+(-1+1)+...+(-1+1)-1
Kasra Mehrafshan yeah,it was obvious.
@@unknownn2412 why? what if we will have 1+(-1+1)+(-1+1)+...+(-1+1)+(-1+1)?
@@Fotelek01 ahh you dont understand lemme show you
In order to have 0=0 we have to equal substance 1 from 1,like this:0=1-1+1-1+1-1+1-1 so we have 0+0+0+0
But the teacher said 0=1+(1-1)+(1-1)+(1-1)....... and he forgot about a final -1 in the end
SS Owl Takizawa there is no -1 at the end because there is no end, it’s infinity
@@imwizzerpvpd1441 yeah but thats only if we take infinity,if we take just a finite number of (1-1)+..(1-1) things change
Hey I just thought of another way to proof 0=1 while watching this. The proof goes:
0 = 0+0+0+0+0+... (an infinite number of zeroes added together)
Hence there are an infinite number of zeroes added together we can rewrite our equation as:
0 = ∞ • 0
Now we can use limits to evaluate ∞ • 0
lim (x • 1/x)
x->∞
As x approaches infinity, x becomes infinity and 1/x becomes 0
Now we also realize that the x cancel out and the final limit we get is:
lim 1
x->∞
There is no x to approach infinity, hence the answer is 1.
Thus, 0=1.
I like this answer. Totally legit!
I always love to have a teacher like you sir! I loved the way how you speak to your students sir !! Huge respect✌️💛💙
Didn’t include the ending minus 1 which still leaves you with zero.
@@melissahaynie3851 There is no end because it's infinite though
For the equation to equal zero, the ones must come in pairs as it does not converge, it is actually periodic. So you cant isolate just the first one, you have to have another minus one to pair with it and complete period or cycle or whatever you call it. Otherwise you would be able to group all the positive ones you wish and repeat the infinite series afterwards and claim it equals any value you want
Tldr: the first guy to object was right
Well that’s the thing about infinite sums, if you rearrange them then yes you can make it equal whatever you want. But that’s not a problem with math or anything that’s something that is well understood so he is allowed to say that the first sum equals zero and the second sum equals one but since he rearranged the infinite sum he cannot say those two sums are equal, which he knows.
@@nathanielroosevelt1489 infinite means here (1-1) is being repeated infinite times not( -1 +1), if first number is 1 last number should be -1, so that it satisfies 0+0+0+0....... He just ignored the initial statement that is 0+0+0+...... and added an extra 1 at the beginning.
@@mr.noname6109 he did not add an extra 1 it’s just that, like you said, (1-1) is being repeated not (-1+1) so even though the notation is the same the sum is not because of the grouping and that’s all I was saying.
@@nathanielroosevelt1489(1-1) or (-1+1) is no different in group or sum. They all have pairs and you can't rearrange that and pretend infinity cancels out your rearrangement, that's all it is.
Crush: you have no chance with me
Me: so I have 1 chance...
Juan Francisco T. 😂 lmao
ROFLMAO🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
Not only one chance but many chances. Because 0=0+0+0+...... and we can prove each individual 0 as 1 by above process. So then 0=anything. Or we can write 0=(2-2)+(2-2)+(2-2)+..... In this way also we can prove 0=anything. So you have any number of chances with your crush. Don't worry hero.
@John Hush
Sir, im a student and i havent any idea about calculus or others.
But i think the error is in the first step .
0 = 0+0+0+0+0+………
Its equal to
0(1+1+1+1+1+……)
👆👆👆
This equal to infinity.
That is, you have multiplied something by infinity.
It is undefined.
Thats why we finally got 1.
Please can you explain this.
Bank : you have $0 in your account
*takes pen*
Me: let me show you that $0 equals one million dollars
People In 1980s- "We will prove that we are better than aliens"
People in 2012-
This guy is a legend
He is still liking our comments
I do my best which is all I can do.
Please continue to watch, share and promote my videos. Thanks so much!
Geometry dash player? :D
CrucibleWreath yup
Let's start by considering the series 0 + 0 + 0 + ..., which is an infinite sum of zeros. We can represent this sum with the mathematical expression:
S1 = 0 + 0 + 0 + ...
Now let's consider the series (1-1) + (1-1) + (1-1) + ..., which is an infinite sum of pairs of numbers that are respectively 1 and -1. We can also represent this sum with the mathematical expression:
S2 = (1-1) + (1-1) + (1-1) + ...
Note that each term in S2 is equal to 0, since 1-1 = 0. Therefore, we can simplify the expression for S2 to:
S2 = 0 + 0 + 0 + ...
We can see that S1 and S2 both represent the same divergent series, and both can be described by the expression 0 + 0 + 0 + ..., but that doesn't mean that they are equal to each other or to any other number.
Even though it may be tempting to take the expression (1-1) + (1-1) + (1-1) + ... and say that it's the same as 1 + (-1+1) + (-1+1) + ..., it's actually not correct to do so. When we distribute the parentheses in the last expression, we change the order of addition and create new terms in the series. Therefore, it's not correct to simplify the expression in that way.
The conclusion is that even though it may be tempting to use algebra to manipulate divergent series, it's important to remember that they don't obey the same rules as convergent series, and that you should be careful about taking expressions out of context.
"But, I don't need those brackets." *proceeds to remove one digit from brackets, continues to use brackets*
Lol u write with a chalk so fast😂
Practice makes perfect?! 😂
jury: you got 10 years in prison
me: observe...
User
0= 1 ?
ChatGPT
The expression "0 = 1" is a mathematical statement indicating equality between two values, where "0" is on the left side and "1" is on the right side. However, this statement is false because 0 does not equal 1. In mathematics, the equals sign (=) is used to denote that the expressions on both sides have the same value. So, "0 = 1" is not correct in any mathematical context.
User
Prove that: 0=1
ChatGPT
Actually, proving that 0 equals 1 is not possible because it's fundamentally untrue in mathematics. In mathematics, equality means that two expressions represent the same value. However, 0 and 1 are distinct numerical values, and there's no mathematical operation or reasoning that can make them equal.
If you're interested in exploring the topic further or if you have a specific context where you'd like to discuss something related, feel free to share!
Isnt 0=1 the largest cardinal in large cardinal tree.
Erm... Where is "-1" in the end?
Форест Дрекстер it goes on infinitely
which end?
Thanks I showed this to my teacher to get me 1 marks where I got zero. I got zero in 7 questions but u saved my 7 marks
That happened
Him: is in debt for $5000
Also him: *so let me show you something cool...*
Him - “So then we just move the brackets…”
No nooo we don’t move the brackets!
I'm afraid you've misunderstood at calculation Mr. Hush 1:05 Here's the thing, the (1-1) thing is infinite so you can't just say that 1+(-1+1)+(-1+1)+... equals to 1+0. You know, you can't define the last number. Even if you will say that it can be defined like 0= (1-1)+(1-1)+(1-1)+(1-1) in the end you will still get 1+(-1+1)+(-1+1)+(-1+1)-1 and is still 0=0
@Amarok How can you know it ends in 1 when you can't define the limit of infinity
@Amarok alright ima explain this as easy as possible. Lets say that you can define the last bracket in this infinity. Its going to be 0 = (1-1)+(1-1)+...+(1-1) and you moved the brackets so its gonna be 0 = 1+(-1+1)+(-1+1)+...+(-1+1)+(-1) which can also be said as 0 = 1+0+0+0+0+...+0+0+0+0+(-1) You know. It comes in pair of (-1+1) so the 1+0+0+0+0+... = 1 is impossible. like if there's 1 infront. then there's -1 at the back
@@katoriwa Yes we can, the definition of the limit of infinity is never ending
Edit: So there is no limit
@Amarok it didnt add -1, THE -1 is always there, but you just can't define it
I agree you however, it is not that you cannot know the last number but that there is no last number because these infinite series are in ordinal space not cardinal.
Actually, I spotted one mistake. Because he is shifting the bracket to the next, he is borrowing the +1 from the next zero.
Which leaves a -1 from the last zero. But he forgot to write it down. If he takes a fixed number of zeros, it will clearly show this error.
0 = 0 + 0 + 0 + 0
0 = (1-1) + (1-1) +(1-1) + (1-1)
What done wrong during shifting is he forgot to write the last -1
0 = 1 + (-1+1) + (-1+1) + (-1+1) + (-1)
0 = 1 + (0) + (0) + (0) + (-1)
0 = 1 + (-1)
0 = 0
There are lots of interesting mathematics in this world... I do appreciate his efforts, because only when people things outside of the box.... New inventions get born.
So I do appreciate his work & inspiration :)
Technically speaking that’s not the thing he did wrong but his proof is still very wrong.
@@stingy5591 well, in simple words that is what he did wrong , tbh !
there is no "last" in infinity sum.
@@handrianoperwira2626 no, there isn't. but we can surely say that the infinith term is 0. his logic is still ryt
@@handrianoperwira2626 ??
If 0=1
And in other video you have proved
1=2
Then according to you
0=2
😏😏😏
He needs to make a vid on that
More like
0=1=2
True
That was my logic too😁😁
Then binary should be converted into trinary
Teacher: you got zero
Me: 100 + (-100+100) +........
Am i the only one here who scrolled thru the comments too look for the smart explanations from other people.
Nope doing it right now
I am actually know what is wrong but I just want to be sure
@@linkmax5374 sure sure
Its an infinite series which diverges, which means there is no way to find the sum, that’s how I learned it at least.
Me too
So if 0 = 1 then we are in 2119
or in 2009
@@lucca3113 oof prefer 2119 tbh
2121 now 😂
We are in 2020 while this guy is in 2121
*?_*
1:31 there is the error, if you group them like that it will be: 1+0+0+0+0+0+........+0-1 so =0
Me: "Why is this wrong?"
Teacher: "The correct answer is 1 but yours is 0."
Me: "Let me prove to you how 0 is actually equal to 1."
Me: “Hey can you give me 0 dollars?”
Friend “Sure??”
Me: “You gave nothing.”
Friend: “Yes I know that’s the point right?
Me: “Let me show you something...”
Will surely try this with my dumb friends xDDDDDDD
😅😅
This proof is not correct
If your maths is good then you can understand it in 3rd step (Last line at bottom of board) in which he is making pairs of -1+1 and at last he miss -1
His pairing is not correct
R/Wooooooosh
@@shailmurtaza9082 thats not the point
Why is *0!=1* ❓
👨🏻💻 *Programmers* : Because 0 is not equal to 1
😁
Ah yes, zero factorial :D
Programmers only think of an "off" and "on" state when it comes to 0 and 1.
Fractional defines the possible variations of the element grouping in one gruop of elements, when there are zero elements in a group you can only group them in one way, im not good at professional math language, so it might be a little bit different from the reality
@@iamnotquitesureifiamrightb7423 fractional?
@@kxt9458 yeah, but my explanation can be inaccurate
For the math experts in the comments: there is no “last” -1, the series is infinite.
The problem is his reasoning only applies to convergent series: the one he used is not among them.
infinity positive one + infinity negative one + infinity zero = 0,whats wrong with this ? why it should be equal to 1 ?
@@alisalimli tit is not infinite positive one) plus (infinite Negative ones) becouse you can not know if there are the same Numbers of positive and negative ones. I mean, if we go to the third term (or any odd term of the serie) , we will obtain 1+(-1)+1= 1, but if we go to te fourth term ( or any even term) we will have 1+(-1)+1+(-1)=0
Infinite is not even neither odd cause infinite is not a number, just a mathematic concept so the second serie does not converge to any number so it is not equal to the first one. The first one you know that it converges to 0 but the second does not converge.
@@edudavila8475 Bro, what you said makes no sense….
There needs to be a -1 at the end of 1+(1-1)+(1-1)… -1, this would be correct. The way he did it was by using a equal sign where you can’t use one because what he did messed with the term….
It does not have to do anything with infinite being odd or not. You substitute a 0 with 1-1, if you multiple that with any natural number (you need to use the natural numbers or else it messes with the term, you can’t use the rational numbers), this will never result in an odd number of 1nes. Meaning what you said in the comment is wrong…
@@sean4706 no no he is right actually 😂 the second series is not a convergent serie so the limit of it doesn’t exist so you can’t add them like that
@@zhangkevin6748
What do you mean with second series
i don’t understand what you mean with that. I corrected Edu d‘Avile because he is wrong. What he said was wrong. He said we don’t know how many 1 and -1 there are, but we know it. At least we know there has to be the same number of them.
The 1+(-1)+1=1 can’t exist, or can you explain how there are 2 times 1 and 1 time -1… you can’t.
Even just saying 0=1 is wrong, it’s plain wrong mathematically.
We both know that if you take something wrong you can prove whatever you want with it, it doesn’t matter. It then can be true or false we don’t know.
infinity is fine, the problem is when you rewrite (1-1)+(1-1)+... as a summation, you get sigma( (-1)^n ) so really what you don't wanna mess with is a negative number raised to a variable. try graphing this.
At 1:25, there is supposed to be a -1 (at the end of the series. Which even though doesn't seem to end, but when the sum of the zeros is done is done, it will appear) which would cancel the first 1 and would result in 0.
Someday this dude is gonna prove that earth is flat 😂
@myths destroyer lol
@myths destroyer you are joking right?
@myths destroyer ummmmm..... ok? You know gravitation existed and still exists right?
myths destroyer uhmm? Ok??
myths destroyer lol i knew you were not that stupid i was just playing around in your play if you were that stupid then you probably wont be able to write comments
The minus 1 in the last bracket doesn’t have anything to pair with so it automatically goes to the plus one, resulting in a zero
It's not that simple since there an infinite number of 1's and -1's. Infinte series follow different rules than finite ones.
John Hush but won’t there always be a left over - 1. You’re talking about infinite. But even with these rules you will always have a minus one that will be pared up with the plus 1 at the beginning. Like a circle, no end no beginning, it just goes back to where you start. I would still think this is correct
@@lorenzolevi5402 it doesn't make sense to talk about something left over in an infinite series; there's no end to it so there's never anything left over
@@mrjohnhush You grouping 10s of (1-1) but in the grouping there is an unpaired 1, it means that if I want to go back one step before the grouping, I will not get to it unless I draw back one 1 from the... 1
@@sisaxazana309 the problem is you can't claim that there will be an extra - 1
For example you can't find the largest positive number
There might be an extra - 1, there might not be
That's the actual answer that we don't know what happens at infinity
Infact we don't even know if adding infinite number of 0s will give 0 or not
For those who couldn't understand...
In the 2nd line, you can see there are ten number of 1.
But while writing the 3rd line, he has started the expression with +1 ended it with +1 and the number of 1 counts upto 9, that is he has not fulfilled the expression with the previous one. So he reminded with +1 at last..
The main trick here is that, the more the number of 1 you are writing, the more trickier gets the equation and easy is to fool others
My maths teacher showed this to us in high school too. I always really likes this proof because it so neatly diverts attention to the wrong place. It seems so obvious that shenanigans are going on when you move the brackets that people completely forget to think about the casual and seemingly logical assertion that 1-1+1-1+1-1... = 0.
My maths teacher showed this to us in high school too. I always really likes this proof because it so neatly diverts attention to the wrong place. It seems so obvious that shenanigans are going on when you move the brackets that people completely forget to think about the casual and seemingly logical assertion that 1-1+1-1+1-1... = 0.
bro you are from which country ???
@@trixieofthetrade7494 no one said it was tho
@@trixieofthetrade7494 Think of it as adding -1 then
@@trixieofthetrade7494I think the wrong portion is how he grouped it. (1-1) + (1-1) turns into (-1-1)(-1+1) which effectively produces 0. How he got that, I have no idea, but it is completely wrong since x + (x-x) = x so in any local sense this form of grouping is wrong.
I got here after watching Modern Family's S10E21 haha
I think the problem here is the use of an infinite series to prove 1 = 0
When you say 1 = 0 + 0 + 0 +... and then 1 = 1 - 1 + 1 - 1 + 1 - 1... you end up with Grandi's series Σ(-1)^n which is a divergent series and has no sum, at least in the usual sense.
Love your videos John!
Of course you're right about the fallacy. Thanks for the compliment. Please share and promote my video and channel. 😎💙🤗💓✌
Actually it's more the fact that the structure of divergent series is not a group (endowed with addition) means that you literally can't manipulate divergent series with + or -
(btw i'm not a native english speaker it may be the wrong mathematics name)
Maths
Albert polynomial
ruclips.net/video/1dhTGpc0mHQ/видео.html
One time must see...
I dont understand ;_;
Try telling a computer that 0 = 1
False
AS a programmer, I can tell you that equates (or evaluates) to false\
If you want an infinite loop, try while (0!=1) { ... }
Quantum computer maaate :D
Nonononononononononononononononononononononononononononononononononononononono
*S Y S T E M O V E R L O A D*
var Zero =1;
There you go.
Don't know whether this is correct or not but that's a Geometric progression right there: 1,-1, 1,-1....
And the sum of a GP is given by a(1-r^n)/(1-r), where a is the first term and r is the common ratio. So, here, a=1, r=-1
If we take n to be an even number we get, 1(1- (-1)^even number)/(1-(-1))=0.
But if we take n as an odd number, we get 1(1-(-1)^odd number)/(1-(-1))=1.
It all depends on how many terms we are considering in the series.
Judge: 1 year in prison for u
Me:
No one commented so...
@@vedparikh26 thanks bro
sorry but what he solved is wrong.....the identitity a^2 - b^2 = (a+b)(a-b) is only applicable when a is not equal to b.....therefore it is wrong...
Numbers: *exist*
This guy: No, we don’t do that here.
🤣🙏🙏🙏🙏
Unbelieveble, he's still liking comments and this after 8,5 years. Respect to this genius!
Unfortunately not your comment. 🤣
@@AjayJain-ef2mz lol
You mean 8.5
It is wrong because the lecturer had used the brackets incorrectly when transitioning from (1-1) + (1-1)+(1-1)+.... and then saying that 1+ (-1+1)+(-1+1)... We clearly see the change of the use of brackets changes the nature of the sum. Meaning (1-1)+(1-1)... Is not equal to 1+(-1+1)+(-1+1). Additionally, we see the reason that the second sum is equal to 1 is because it has an extra term like my previous example (1-1)+(1-1) has four numbers whereas 1+(-1+1)+(-1+1) has 5 numbers. I hope this makes sense
The issue here I think is that this sum isn’t convergent, so it won’t ever give you one definitive answer, causing this unintuitive answer.
Correct! ✌🎓🤗💙
@@mrjohnhush Doesn't it mean, 0 can be everything?
@@orencikensoleta414 Probably yes but not the exact answer would be the answer.
May b the concept of real analysis
1 = 1 + inf*0
Does NOT equate to
1 = 1 + inf*(-1+1) -1 = 1-1 = 0
Changing the repeater is flawed. That's like saying the sum of infinite whole pizzas, without cutting any, results in a bunch of whole pizzas and a half of one. The only way you'd get that half is by cutting a pizza, and that's exactly what he did.
You can disprove this since every 0 = 1-1, but when he takes out that "1", he is going to have to take out "-1" at the end of the infinite sequence. This would give 1 + (-1+1) + (-1+1) + ....-1, which equals zero.
Yes thank you we understood when the 100 other angry people who thought they were smart said it
There is no end in an infinite sequence. The real problem is
(1-1)+(1-1)+(1-1)+... = 0.5 and not 0
@@lcz9547 not true at all lol
yeah if you go on mathologers video they explain properties of infinite series and how changing parentheses in one completely changes the meaning, that’s how people screwed up with the 1+2+3+4... = -1/12
@@commie281
A=1-1+1-1+1-1...
1-A=1-(1-1+1-1...)
1-A=1-1+1-1+1-1...
1-A=A
1=2A
1/2=A
(I don't have enough skill in English to explain that, hope you will understand)
Came here after watching Modern Family in the one where Alex was going to receive a graduation.
Lets just wait for infinity war this 27th april
*-not-* *everyone dies*
I was about to laugh but then I remembered what actually happened in infinity war
arevev SABO-kun
watching this in 2019
Waiting for Part 2
@@jaykody3022 lol
I would be so happy if this guy would be my teacher. You can see how genuinely see how excited and proud of his work this guy is
Infinity + 1 = infinty
Divide that with infinity and u have 1=0
D3rb0fr0stm4nn no than you have 1 = 2
But you can’t divide infinity with infinity tho
Jill Dekeyser i know i just subtracted 1
Jill Dekeyser no really?
First of all, Infinity is not considered to be a number
And second, dividing a number with itself doesn't give you 0, it gives you one, so if infinity was a number, dividing with it would give you:
1 + 1/infinity = 1