Actually, it is infinity. If you put an infinity as the last number, and represent it as N, the top ends up as (1+2+4+8+16+...+2N) Since everything gets cancelled except for the one and the N after subtraction (2N-N), the end result is actually infinity. True because it has been proven that some infinites are larger than others.
No, your original intuition is completely right. He IS still wrong and the result does not hold. Sure, he might have seen a power series that seemed to have this answer (I'm guessing it was (1-2x)^-1). If x = 1, then you get -1. And the power series expansion is 1 + 2x + 4x^2 + .... +(2x)^n, and when you plug in x=1 it appears 1+2+4+8+...= -1. Which is still wrong. The power series only converges when |2x|<1 which means |x|<1/2 has to be true or else it diverges.
It is true that there is some significance to the fact that (1-2x)^-1 as a function equal -1 when x = 1. However, -1 cannot be considered a sum in the usual sense.
.....where did he get the negatives at..... here was adding 1+2+4 so on and then randomly pulled -1-2-4 so on out of his ass and added it to the string of positive numbers
It doesn't work because the series isn't convergent. The point is, it seems to equal -1 because you haven't finished the calculation. If you could show that the series is convergent, then you could use the limit to show the calculation stops changing and thus is done. But you can't with this series. My HS calc book covered this type of fake proof.
But you cant' add (2+4+8+16...) with (-2-4-8-16...), can you? It's an infinite series, so that would be like subtracting infinity from itself even though it's not a number, just an entity. So infinity can't equal -1.. right?
@goej42 you are completley right. I asked my abstract algebra teacher and she said the same. All the idiots saying you are wrong are frikin hypocrites for not actually looking at the vid to see what you mean.
@goej42 Apologies if your already know this, but in higher level math it *is* accepted that infinite divergent series sum to values such as this. Quantum Field Theory using applications of the Zeta functions regularization is an example. where 'real life' actually make use of unexpected results like this, which I assume why MinutePhysics put it here..
*this* 'proof' not a very strong contender, but look up 1+2+3+4+... on wiki then some of Euler or Riemann's work. Its mindblowing!
@Racoonieboy You are right in the sense infinity isn't a number. But infinty is treated as a direction. It means it goes on. It isn't a number itself. It is just an arrow or ellipse (...)
I don't like this proof. I now its supposed to be basic, but if we use the distributive property between the sums within the parenthesis, you'll see that you're left with -1 AND 2 times the last term..let's call it "n." If you're last term is Infinity, then you have (2 x "infinity" -1) which is INFINITY and NOT -1.
You people seem to be confused, let me help you people out. Infinity is NOT A NUMBER. You cannot treat it as such, you cannot expect infinity to be there at the end, because there is no end. This also means that this video is valid, because with no end, there is no extra number at the end that makes it invalid.
@Racoonieboy In certain sense this series does sum to -1, but this is not how to prove it.
There's always a number at the end that you can't cancel out, as there are infinite terms each with specific value getting bigger as you go to the right.
In other words: every time you cancel out a pair that has been 'shifted left' on the bottom, add a number double to what you have just canceled. (if you don't do this every time, you haven't actually shifted anything to the left)
This method should work for infinite series like 10+20+40+80+... and 100+200+400+800+... etc (multiples of 10 of this series) with answers of -10 and -100 etc
Are the answers for zeta regularized results the same?
I've been getting a lot of replies about my post. I will clear some things up. The reason why I said you have to line them up is because the way he's doing it, the top will always be a step ahead. Again refer to 0:29. -1 at bottom is the n=0 term. 2 at the top is the n=0 term. The way he writes it, he is assuming the top will be a step faster. It's not the case. For both top and bottom, the value of n will increase at the same rate. That's why you have to group them. At n=10, 2^10 - 1.
Cool your baffles people, this is just a fun way of showing that you can't "just" plug infinite numbers into standard math and expect a result that makes sense.
Ironically, one part where he's wrong is the "1*x=x for all x". This is not the case; that holds for all *real* x. And the infinite quantity he tried to apply it to is not such a number.
I think I'll stick to VSauce and C.P.G. They use facts and don't try to bend any rules, especially not math of all things. As a supposed physicist, you should know that what you do to one side of an equation, you have to do to the other, so pretending that there is an empty space where the 1 should cancel out the -1 is absurd. You would've been better off claiming it equals 0 then saying it equals -1, but you still would've been wrong, so why even upload this video? Oh yeah, for the money...
@Blake69able As someone who is supposedly able to see this video, you should know that they are both the SAME side of the equation. Your point here makes no sense.
The positive parts contains all the same terms as the bottom part except the "-1". Plus, addition is commutative; therefore the order in which you add the terms on the same side of the equation do not give a different result.
The first infinity ,being undefined, cannot cancel out the second infinity ,it too being undefined. Thus we are left with -1+ infinity which is infinity.
This is so dumb. The -1 most certainly does cancel out. If you add all the terms after distribution you get 2 + (-1) + 4 + (-2) + 8 + (-4) + 16 + (-8) + 32 + (-16) = 1 + 2 + 4 + 8 + 16 + ...
It does not change anything, it's just multiplying by 1. You can't just leave the -1 and cancel out the rest of the terms because it's convenient. NOOBS
@jason651294 Addition/Subtraction are defined as having the property of associativity. This means that order in which you deal with the terms are proven to give a mathematically consistent answer. This is like saying that (2-1)-2 does not equal (2-2)-1.
@Raztheeccentric Read what you're replying to. The result actually is different. As is the case once again, addition and subtraction are associative... IN THE RING OF REAL NUMBERS. Infinite quantities are not in the ring of real numbers.
For people who aren't into math, let me try to explain why he is wrong. And it's very simple. Refer to shot at 0:29. You see how he's cancelling those numbers out? But he shifted all the numbers on the top to the right by one. Technically, 2 should be above -1. So if you were to rewrite what he just did by putting 2 above -1, and continue his 'pattern, we'll cross out every number except an EXTREMELY large number (infinity) at the top, and -1 at the bottom. Therefore adding up to infinity
@goej42 But that doesn't matter. The top can be rewritten as the Sum from 2->infinity and the bottom is -1 - (Sum from 2-> infinity). Both sums cancel.
@goej42 Just to expand on my comment, addition is defined as a commutative process. This means that the order in which you add terms should not affect the result of the operation. The positive part contains the exact same terms as the negative terms other than minus one. If it went to a non-infinite limit then there's be a missing term, but since it doesn't its mathematically consistent to pair up the identical terms before touching the -1.
@Raztheeccentric You are right. The order in which you add the sums is insignificant. But the way he adds creates an illusion. The reason why I said you have to line them up is because it will help clear up this illusion. Let's consider a really high number. n=1000. Once you cancel everything out, you will be left with 1000 at the top and -1 at the bottom. Thus you will have 999. Same applies for a really high number like infinity.
@goej42 No, this argument is incorrect. The set of natural numbers is infinite so there's never a left over term. It also doesn't contain infinity, so every element is a finite number. Infinity is not a number.
If you were to create a Venn diagram where one set was "all possible values for 2^n" and the other was "all possible values for 2(2^n)" the second set would be a subset of the first; it would contain every element except "1".
@goej42 I made a mistake, it should be 2(2^n) - 2^(n+1) = 0. Also, to be completely clear, n is a natural number. In the examples I give.
Basically, you can't treat infinity as a number so large that mathematics breaks down when you get to it. There isn't suddenly a number so large that you can't take it away from itself.
@Raztheeccentric His equation above was 2(2^n) - 2^n. That is equal to 2^(n+1) - 2^n. Because it's impossible to treat n as infinity to solve this equation, we use lim as n-> infinity. Like I said before we have to compare n to really high numbers to see a correlation and a pattern in this equation. If we substitute n as 1000, 100000, 10000000, we'll see that the the equation will equal to a ridiculously high number. We must assume when n is replaced with infinity, infinity will be the result
@goej42 The problem is that "infinity" isn't a number, and whatever that extremely large number at the top is, you can multiply double it by -1 and cancel it out. This weirdness happens because there is no limit on numbers, there is no "biggest" number out there so there can not be something on top. I think the take away lesson should be that trying to work with an infinite series makes normal mathematics break down.
@goej42 Except that the EXTREMELY large number will always be cancelled by the next term in the negative series. You only end up with a large number at the end if you truncate the series somewhere, making the series finite instead of infinite.
@goej42 I think he shifted the numbers over because 1 and -1 cancel, resulting in -1. He just did not write in the 1 and instead left the space blank.
@superfatkid100 That's where the illusion lies. At n=0, its 2 for top and -1 for bottom. All the terms at n=0 should line up. At n=1, it's 4 for top and -2 for bottom. These should line up. If you continue and group all terms of n, you will find that everything will cancel out EXCEPT 2^n (as n approaches infinity) and -1 to cancel out. The fact that he doesn't group the n'th term together creates an illusion that they all cancel out except -1, however the top will always be a step ahead.
@goej42 but you can never get to that EXTREMELY large number as the series continues to infinity.... so im sure that argument doesn't hold. apologies if im wrong.
@wtfyman I'm just saying extremely large number because we can never comprehend infinity. If you will, 'as limit n approaches infinity' is a more accurate term.
@goej42 actually superfatkid is right he just didnt bother to write the other 1 in and besides even if you were right you would still end up with infinity = -infinity which still breaks math :D
@goej42 Really? What you pointed out had nothing to with math (distributive property maybe) it was more about how he wrote down the numbers. Higher maths have shown that the specific infinite series he is referring to can be assigned the value -1 as that is more usable than an infinite series. Don't claim he is wrong because you do not understand what he is talking about, the video was a clever way to introduce people to some things done in higher level math. The series can be infinity or -1.
@goej42 You and all those upvoting you obviously don't understand the concept of infinity. Infinity+1 is still equal to infinity, so there is no "shift." What this video portrays is actually accurate, just like how .9999..... (repeating to infinity) is exactly equal to 1.
@goej42 No, no, he's got it right. And wrong. You can use the same logic to say it equals infinity. (-1 + 1 + 1) = -1,-2,-3... + 1,2,3... +1,2,3... yields 1,2,3...
The problem is that "infinity" and "numbers" are different. What you said would apply to a finite series of numbers, but "infinity" is an abstract concept of numbers, which is weird because numbers themselves are abstract.
However, this is infinity. Both series of numbers stretches infinitely with no end, which is the "same end". It can be represented (though not defined) as 2, 4, 8, 16, 32... to the "same end"
-1, -2, -4, -8, -16, -32... to the "same end"
which all cancels out except '-1'.
Again, the ultimate issue here is infinity is not a number in the way we usually mean.
@goej42 It's not wrong. Your reasoning is incorrect. Since there is no limit, there can be no extremely large number (infinity is not a number) and therefore this is still valid.
@goej42 except since both series go to infinity there is not a finite very large number in the end of either. Basically the fact that the starting seiries is 1 step ahead matter only in the event that you have a difinitive end point. If you can not define the end member of the sequences you are left with just "-1".
OMG EVERY1 iz S0 smRt lol i wish i wus dat intelect. Does everyone have to reply with a paragraph? And it's a cute concept, but if you honestly feel the need to point out the fallacies that are apparent within, your dick is (2-1){1,2,4,8,16...} inches long.
Infinity is just as 'weird' as Zero as far as I can tell. Infinity and Zero stay the same no matter what you do to them. There is no 'Half-Infinity' or 'Two-Infinity' just as there are no 'Half-zeroes' and 'Two-zeroes'. However, let's do some 'creative math': Infinity = (2 - 1) x Infinity? We can also write this as: Infinity = (2 x Infinity) - (1 x Infinity) ... Wait a Minute! 2 x Infinity is still Infinite thus Infinity! So, Infinity = Infinity - Infinity, so Infinity = 0? Infinity = -1 AND 0?
@Zelalas Yes, that's what happens when infinite numbers are used as though they are the same kind of thing as integers or 'real' numbers. They are not. Compare, for example, saying Egg-Magnet=Despair, and concluding that magnet is a very weird number indeed. Rather, the operations you're using (+,-,*... as used with, say, integers) only have defined meaning with a very specific set of inputs. "Infinity" is not one of them, just as 'magnet' isn't, or 'the set of negative integers.'
@dymaseran Yes, but this video, in my eyes, treats them as such, Why? In the above case 2 numbers would remain after the cancellation process if infinitely positive numbes cancel out infinitely negative numbers by using 2-1 . -1 and the 'Highest number' which is, you guessed it, Infinitely large. Thus the answer would not be, -1 but - Infinity.
However, - Infinity does not really exist, as infinity is not a number. - Infinity is still Infinity as both are the same thing, just one is 'backwards'.
@Zelalas But there is no final number. That would be true in a finite sum but in an infinite sum all terms but the number 1 are present in the positive part. Unless you define a bound on the set of natural numbers there will always be a non infinite number - a non infinite number. The natural numbers don't suddenly become infinity. Unless you add exceptions to the distributive property of multiplication or the associative property of addition this video is mathematically consistent.
@Raztheeccentric True, but this is the problem and why you cannot just say: 'I do this and voila! The sum is -1!'. As I stated before, try using 3-2. It doesn't work the same way anymore. Exceptions are already in place.
Also, it should say this: {2-1,4-2,8-4,16-8 ....}
The inherent problem here is that we shift one sum, the negative one, off by one number when we actually shouldn't do that, just so we can get the -1. This is only possible because Infinity is not a number you can reach.
@Zelalas Shouldn't isn't the same thing as "can't". You're right in that you "shouldn't" have an infinite sum of positive numbers equal to -1. In fact, it can be proven that using the addition operator on only positive numbers you can only get a number greater than any of the original numbers. Likewise, as you said using 3-2 you get a different answer, which "shouldn't" happen either.
But the method itself is not incorrect. The result is impossible despite of a correct method.
@dymaseran Also, 3 - 2 = 1, thus... {3,6,9,27,81....} cancels out with... {-2,-4,-8,-16...}! Wait a minute.... How come infinity now has a Infinite answers?
Also, If I got anything wrong, feel free to correct me! (I know you will, this is the Internet!)
@Zelalas no. infinity - infinity is not 0, its undefined. Look up Hilbert's Hotel or watch To Infinity and Beyond - Horizon - BBC.
also infinity doesn't equal -1 either, the series 1+2+4+8+16+...+2^n does - if you use the Zeta function. That is what this video was trying to convey. The series 1+2+3+4+5+... n = -1/12 as n tends to infinity.
Math does not allow simple arithmetic like on divergent series, if you could you end up with the answer 2^n-1 where n tends to infinity.
@0001robm Ah, my mistake. I was under the impression that. the series 1+2+4+8+16+.....+2^N had the answer: ( 2^(N+1))-1. Thus 2^N+1 would have to become 0 for this to work. So if 2^N+1 is Infinity and we need a 0 for this this work.....
Also, What happens if you try using 3-2 instead of 2-1, same results?
@Zelalas 2^n (where n is becoming infinitely large) is basically a large positive number. since n is infinitely large it doesn't matter if its n, n+1,n+1000 etc as its the largest natural number.
@Zelalas 1+2+4+8+... should also give a large odd number (if using basic arithmetic)
if this is allowed (an apparently its not) 3-2 will give the same result
btw first time i saw this video i wasn't really convinced either, but string theory etc are based on extremely complicated math that with divergent series.
Euler 400 years ago 'proved' the sum of natural numbers is -1/12.
if you go to wolframalpha com and put in 1+2+3+4+... and look at the regularized result
I had to watch that twice to see exactly what he did there. That is crazy. I am utterly astounded and can't find a single argument to disprove that. Infinity really fucks with math sometimes.
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
Watch this: (4-2-1)*(1+2+...) = (4+8+...) - (2+4+8...) - (1+2+4+8...) = -2 - sum(2^n | n -> infinity) = -infinity I think we all know this video is bollocks. The reason it's bollocks is because the sum of a divergent, infinite series is not discrete, so you can'd subtract discrete numbers from it. Some people will tell you that: infinity - 1 = infinity. This is WRONG. Subtracting 1 is not a valid operation on infinity, because infinity is not a number. infinity - 1 = gibberish
This would be correct IF ONLY THE NUMBERS HAD A LIMIT. When you multiply the (2-1) with the (1+2+4+8...) you should keep in mind that you multiply the 2 and -1 with the SAME AMOUNT OF NUMBERS but since they are infinite then when you get to
= 2+4+8+16
-1-2-4-8-16 you CANNOT cancel them out because as you can see there are 4 numbers in the upper row but 5 numbers in the bottom one. I hope you understood my point of view. However if I am wrong please point out my mistake.
@bboylayz So just to beat a dead horse: the point is, infinity doesn't have a speed or time, it exists forever so trying to distribute it at a set point in time doesn't quite make sense. But when thinking in terms of matching up equal but opposite numbers to cancel them out, there is always a matching number on the other side of the distribution in the world of infinity except for negative 1.
This actually does make sense when you are talking about infinity. Took me a second to realize he didn't use the same amount of numbers while distributing, and then it made sense. This was intentional, and the best way to think of it is that infinity has no last number. So as you keep going, every number in the pattern has (or EVENTUALLY WILL HAVE) an equal but negative value to cancel it out when distributing the 2 and -1 (in 2-1)... That is every number but -1.
Nice video, but it overstates the actual result. In the usual sense, the summation is certainly infinite. The summation also behaves in some ways as the finite integer -1, and so there is some rationale for treating it as such. But, it is an overstatement to say that the summation equals -1. As @superkoopasirf suggested earlier, I also recommend googling '1+2+4+8 wiki'.
@japanboogie Let me try explaining: 1+2+4+8+etc... is nothing but (1)(1+2+4+8+etc) because we're basically multiplying the equation by one. Now this means we don't necessarily have to multiply the LHS by 1. Yeah?
Now, 1=2-1. Hence we can write the previous equation as: (2-1)(1+2+4+8+etc). Now simplifying the brackets: (2+4+8+etc.) - ( 1 -2-4-8-etc.) = -1.
Nearly every comment is saying how this doesn't work. People need to understand there's more to mathematics than just the real numbers. Complex analysis, get to know.
In fact he used the equation of sum to infinity. S( ∞)=a/(1-r) where a is the first term of the sequence while r is the common ratio of the terms( 1/(1-2)=-1). However, this equation only applies under condition of -1<r<1. Obviously, 2 is out of range. Try to download "Graphmatica", a graph plotting software, and type"y=(1-(2^x))/(1-2)" , which is the equation of sum of geometric sequence ( S(n)= a(1-r^n)/(1-r))and hit enter. Sure you'll find that the graph keep increasing up to infinity.
you shifted the negative values to the left which is deceptive, cus the -1 is still there, but then 32 would be on the top, giving a sum of 31 at the 5th term
@hgeorgehful No, that's simply not how it works. There is no 2^inf term. The sequence 1,2,4,8,16,... contains every term which the sequence 2,4,8,16... does, but also contains the additional term of 1. Trust me, I'm a masters student in math.
...and very quickly so as a certain emperor found out when he lost all his rice. BUT, when mathematics starts to get fuzzy, interesting things happen. Don't loose faith in OMF ;)
Actually, Wikipedia does confirm he's not completely insane! According to the encyclopaedia, it really is negative one. Just Google '1+2+4+8 wiki' and you'll find the page.
If you want something nifty and actually correct, how's about the fact that 0.9999...=1. That's pretty cool when you prove it. 1=3*(1/3)=3*0.3333...=0.9999...
There is just one thing I don't understand and would like an explination. How is he able to move the negative two over one so that -1 isn't subtracted from it? In other words, why doesn't he subtract -1 from 2? He instead moves the top equation over one position, why?
@ideedkindsir I agree with you. He uses visual similarity to position the numbers- it only LOOKS logical. Thus the fooling, because -1 should be actually under +2 as you stated.
Yeah, -1, right. This could be a nice way to show it's more like 2^(n+1)-1, which is also really easy to show by induction. It really hurts to watch this.
He did not put a positive 1 at 0:27, so obviously when he cancels out everything else -1 will be the only term left over. What did positive 1 ever do to you, bro?
Actually, it is infinity. If you put an infinity as the last number, and represent it as N, the top ends up as (1+2+4+8+16+...+2N) Since everything gets cancelled except for the one and the N after subtraction (2N-N), the end result is actually infinity. True because it has been proven that some infinites are larger than others.
fizaan95 10 hours ago
what i dont understand is where the 1 on the right goes.what im doing is: 2*1=2
-1*1=-1
2-1=1
when he adds the other side, it should cancel out. can anyone explain this to me?
idontevenhavestuff 11 hours ago
adding past infinity
infinity+1
bipbop4232 15 hours ago
Comment removed
phoskins 15 hours ago
This has been flagged as spam show
@0001robm
No, your original intuition is completely right. He IS still wrong and the result does not hold. Sure, he might have seen a power series that seemed to have this answer (I'm guessing it was (1-2x)^-1). If x = 1, then you get -1. And the power series expansion is 1 + 2x + 4x^2 + .... +(2x)^n, and when you plug in x=1 it appears 1+2+4+8+...= -1. Which is still wrong. The power series only converges when |2x|<1 which means |x|<1/2 has to be true or else it diverges.
phoskins 15 hours ago
@0001robm
It is true that there is some significance to the fact that (1-2x)^-1 as a function equal -1 when x = 1. However, -1 cannot be considered a sum in the usual sense.
phoskins 14 hours ago
Comment removed
phoskins 15 hours ago
my mind just got blown away
wazscience 18 hours ago
you have an extra digit at the bottom
jjlohsna 20 hours ago
.....where did he get the negatives at..... here was adding 1+2+4 so on and then randomly pulled -1-2-4 so on out of his ass and added it to the string of positive numbers
JLSP619 20 hours ago
@JLSP619
I assume you're in elementary school if you can't understand where he got his negatives.
We know: One times any number equals that number. Two minus one equals one.
Therefore, when you multiply (2-1) against infinite series and distribute the 2 AND -1, the negative one produces negative numbers.
killjbieberplz 12 hours ago
-1 is the score you had on your math tests
vnature101 21 hours ago
so does infinity - infinity = infinity?
cubedude76 22 hours ago in playlist MinutePhysics
@cubedude76 Unfortunately, infinity - infinity is undefined.
SayyWhaaaaat 18 hours ago in playlist MinutePhysics
Troll maths, maths you wish weren't true
ishitcrockets 1 day ago
It doesn't work because the series isn't convergent. The point is, it seems to equal -1 because you haven't finished the calculation. If you could show that the series is convergent, then you could use the limit to show the calculation stops changing and thus is done. But you can't with this series. My HS calc book covered this type of fake proof.
gregmdunn 1 day ago
(2-1) is not the same as (2)(-1)
TheMightyWeave 1 day ago
@TheMightyWeave
I can't see where anyone said that it was...
Qw3rtypop 1 day ago
But you cant' add (2+4+8+16...) with (-2-4-8-16...), can you? It's an infinite series, so that would be like subtracting infinity from itself even though it's not a number, just an entity. So infinity can't equal -1.. right?
XxmynameboratxX1 1 day ago
i watched it like 4 times and still couldnt understand it
GatorFog 1 day ago 2
you might be good, but you are no vihart
MrSister127 1 day ago
Infinite sums are not commutative, that's all there is to this.
meestryal 1 day ago
1+2+4+8+...+infinity+infinity
=1(1+2+4+8+...+infinity+infinity)
=(2-1)(1+2+4+8+...+infinity+infinity)
= 2+4+8+16+.........+infinity+infinity
-1 -2 -4 -8 -... -infinity -infinity
=infinity-1
=infinity not -1
15october91 2 days ago 2
@15october91
You misunderstood a step. 0:22 is the 2(1+2+4+...), it just has a different alignment.
Qw3rtypop 1 day ago
that's the same as:
1+infinity = infinity /-infinity
1=0
-> infinity is no number
andoriz0r 2 days ago 2
every minute a guy tries to covert me to Mormon
haigfeinn 2 days ago in playlist MinutePhysics 2
@goej42 you are completley right. I asked my abstract algebra teacher and she said the same. All the idiots saying you are wrong are frikin hypocrites for not actually looking at the vid to see what you mean.
iced199 2 days ago
@iced199 Thank you, you are the only one that has said that too me so far. :)
goej42 2 days ago
@goej42 Apologies if your already know this, but in higher level math it *is* accepted that infinite divergent series sum to values such as this. Quantum Field Theory using applications of the Zeta functions regularization is an example. where 'real life' actually make use of unexpected results like this, which I assume why MinutePhysics put it here..
*this* 'proof' not a very strong contender, but look up 1+2+3+4+... on wiki then some of Euler or Riemann's work. Its mindblowing!
0001robm 1 day ago 7
@Racoonieboy You are right in the sense infinity isn't a number. But infinty is treated as a direction. It means it goes on. It isn't a number itself. It is just an arrow or ellipse (...)
iced199 2 days ago
You should acknoledge your mistake and be a man.
ffxme 2 days ago
I don't like this proof. I now its supposed to be basic, but if we use the distributive property between the sums within the parenthesis, you'll see that you're left with -1 AND 2 times the last term..let's call it "n." If you're last term is Infinity, then you have (2 x "infinity" -1) which is INFINITY and NOT -1.
davenatal86 2 days ago
You people seem to be confused, let me help you people out. Infinity is NOT A NUMBER. You cannot treat it as such, you cannot expect infinity to be there at the end, because there is no end. This also means that this video is valid, because with no end, there is no extra number at the end that makes it invalid.
Racoonieboy 3 days ago
@Racoonieboy In certain sense this series does sum to -1, but this is not how to prove it.
There's always a number at the end that you can't cancel out, as there are infinite terms each with specific value getting bigger as you go to the right.
In other words: every time you cancel out a pair that has been 'shifted left' on the bottom, add a number double to what you have just canceled. (if you don't do this every time, you haven't actually shifted anything to the left)
0001robm 3 days ago
This method should work for infinite series like 10+20+40+80+... and 100+200+400+800+... etc (multiples of 10 of this series) with answers of -10 and -100 etc
Are the answers for zeta regularized results the same?
0001robm 3 days ago
Dude, stick to physics cuz your math sucks.
EliteGamerXX 3 days ago
He forgot the order of operations... Nice vid though :)
CmdrStewy 3 days ago
I've been getting a lot of replies about my post. I will clear some things up. The reason why I said you have to line them up is because the way he's doing it, the top will always be a step ahead. Again refer to 0:29. -1 at bottom is the n=0 term. 2 at the top is the n=0 term. The way he writes it, he is assuming the top will be a step faster. It's not the case. For both top and bottom, the value of n will increase at the same rate. That's why you have to group them. At n=10, 2^10 - 1.
goej42 3 days ago
@goej42 infinity that cancels out with negative infinity
DarkKnight3495 3 days ago in playlist MinutePhysics
I like to do this kind of things to trick my friends! I remember when I made the believe that 2=1 xD
AschKris 3 days ago
what
fdoraman122 3 days ago
O.o many people are saying you're wrong!?!?! IS THAT TRUE????
But still I still remain subscribed because you're vids are so amusing to watch
Adrian8bit 3 days ago
What just happened.
Ps the other day my lecturer told us that addition doesn't work if you try to do it to infinity. Maybe this is why.
harryh111111 3 days ago
Cool your baffles people, this is just a fun way of showing that you can't "just" plug infinite numbers into standard math and expect a result that makes sense.
tabaks 3 days ago 15
It's a subtraction of infinities,which in math theory is an undefined operation to avoid fallacies such as this or many others
gorospakabum 3 days ago 2
Ironically, one part where he's wrong is the "1*x=x for all x". This is not the case; that holds for all *real* x. And the infinite quantity he tried to apply it to is not such a number.
dymaseran 4 days ago
There was a math warning, but I've seen no math in the video.
Dresu87 4 days ago 4
@Dresu87 Win.
dymaseran 4 days ago
I think I'll stick to VSauce and C.P.G. They use facts and don't try to bend any rules, especially not math of all things. As a supposed physicist, you should know that what you do to one side of an equation, you have to do to the other, so pretending that there is an empty space where the 1 should cancel out the -1 is absurd. You would've been better off claiming it equals 0 then saying it equals -1, but you still would've been wrong, so why even upload this video? Oh yeah, for the money...
Blake69able 4 days ago
@Blake69able As someone who is supposedly able to see this video, you should know that they are both the SAME side of the equation. Your point here makes no sense.
The positive parts contains all the same terms as the bottom part except the "-1". Plus, addition is commutative; therefore the order in which you add the terms on the same side of the equation do not give a different result.
Raztheeccentric 4 days ago
The first infinity ,being undefined, cannot cancel out the second infinity ,it too being undefined. Thus we are left with -1+ infinity which is infinity.
shailend4000 4 days ago
This is so dumb. The -1 most certainly does cancel out. If you add all the terms after distribution you get 2 + (-1) + 4 + (-2) + 8 + (-4) + 16 + (-8) + 32 + (-16) = 1 + 2 + 4 + 8 + 16 + ...
It does not change anything, it's just multiplying by 1. You can't just leave the -1 and cancel out the rest of the terms because it's convenient. NOOBS
jason651294 4 days ago
@jason651294 Addition/Subtraction are defined as having the property of associativity. This means that order in which you deal with the terms are proven to give a mathematically consistent answer. This is like saying that (2-1)-2 does not equal (2-2)-1.
Raztheeccentric 4 days ago
@Raztheeccentric Read what you're replying to. The result actually is different. As is the case once again, addition and subtraction are associative... IN THE RING OF REAL NUMBERS. Infinite quantities are not in the ring of real numbers.
dymaseran 4 days ago
2+2=CHICKEN!!
johnfox454 4 days ago
1+1+2+4+8+16...= 0 ? For some reason that doesn't sound right...
lolziesish 4 days ago
For people who aren't into math, let me try to explain why he is wrong. And it's very simple. Refer to shot at 0:29. You see how he's cancelling those numbers out? But he shifted all the numbers on the top to the right by one. Technically, 2 should be above -1. So if you were to rewrite what he just did by putting 2 above -1, and continue his 'pattern, we'll cross out every number except an EXTREMELY large number (infinity) at the top, and -1 at the bottom. Therefore adding up to infinity
goej42 4 days ago 34
@goej42 Why make it so hard when you can do it easier?
ANiceProduction 4 days ago
@goej42 But that doesn't matter. The top can be rewritten as the Sum from 2->infinity and the bottom is -1 - (Sum from 2-> infinity). Both sums cancel.
Raztheeccentric 4 days ago
@goej42 Just to expand on my comment, addition is defined as a commutative process. This means that the order in which you add terms should not affect the result of the operation. The positive part contains the exact same terms as the negative terms other than minus one. If it went to a non-infinite limit then there's be a missing term, but since it doesn't its mathematically consistent to pair up the identical terms before touching the -1.
Raztheeccentric 4 days ago
@Raztheeccentric You are right. The order in which you add the sums is insignificant. But the way he adds creates an illusion. The reason why I said you have to line them up is because it will help clear up this illusion. Let's consider a really high number. n=1000. Once you cancel everything out, you will be left with 1000 at the top and -1 at the bottom. Thus you will have 999. Same applies for a really high number like infinity.
goej42 4 days ago
@goej42 No, this argument is incorrect. The set of natural numbers is infinite so there's never a left over term. It also doesn't contain infinity, so every element is a finite number. Infinity is not a number.
If you were to create a Venn diagram where one set was "all possible values for 2^n" and the other was "all possible values for 2(2^n)" the second set would be a subset of the first; it would contain every element except "1".
No matter how big "n" gets, 2(2^n) - 2^(n-1) = 0.
Raztheeccentric 4 days ago
@goej42 I made a mistake, it should be 2(2^n) - 2^(n+1) = 0. Also, to be completely clear, n is a natural number. In the examples I give.
Basically, you can't treat infinity as a number so large that mathematics breaks down when you get to it. There isn't suddenly a number so large that you can't take it away from itself.
Raztheeccentric 4 days ago
@Raztheeccentric His equation above was 2(2^n) - 2^n. That is equal to 2^(n+1) - 2^n. Because it's impossible to treat n as infinity to solve this equation, we use lim as n-> infinity. Like I said before we have to compare n to really high numbers to see a correlation and a pattern in this equation. If we substitute n as 1000, 100000, 10000000, we'll see that the the equation will equal to a ridiculously high number. We must assume when n is replaced with infinity, infinity will be the result
goej42 4 days ago
@goej42 The problem is that "infinity" isn't a number, and whatever that extremely large number at the top is, you can multiply double it by -1 and cancel it out. This weirdness happens because there is no limit on numbers, there is no "biggest" number out there so there can not be something on top. I think the take away lesson should be that trying to work with an infinite series makes normal mathematics break down.
Viperzka 3 days ago
@goej42 Nope, you are wrong :P
curtjod 3 days ago
@goej42 Except that the EXTREMELY large number will always be cancelled by the next term in the negative series. You only end up with a large number at the end if you truncate the series somewhere, making the series finite instead of infinite.
thunder4315 3 days ago
@goej42 I think he shifted the numbers over because 1 and -1 cancel, resulting in -1. He just did not write in the 1 and instead left the space blank.
superfatkid100 3 days ago
@superfatkid100 That's where the illusion lies. At n=0, its 2 for top and -1 for bottom. All the terms at n=0 should line up. At n=1, it's 4 for top and -2 for bottom. These should line up. If you continue and group all terms of n, you will find that everything will cancel out EXCEPT 2^n (as n approaches infinity) and -1 to cancel out. The fact that he doesn't group the n'th term together creates an illusion that they all cancel out except -1, however the top will always be a step ahead.
goej42 3 days ago
@goej42 yeah, pitfalls of gaming with the BODMAS rule!
jazzthemystic 3 days ago
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@goej42 yeah, pitfalls of gaming with the BODMAS rule!
jazzthemystic 3 days ago
@goej42 but you can never get to that EXTREMELY large number as the series continues to infinity.... so im sure that argument doesn't hold. apologies if im wrong.
wtfyman 3 days ago
@wtfyman I'm just saying extremely large number because we can never comprehend infinity. If you will, 'as limit n approaches infinity' is a more accurate term.
goej42 3 days ago
@goej42 actually superfatkid is right he just didnt bother to write the other 1 in and besides even if you were right you would still end up with infinity = -infinity which still breaks math :D
migratorycocanut 3 days ago
@goej42 Really? What you pointed out had nothing to with math (distributive property maybe) it was more about how he wrote down the numbers. Higher maths have shown that the specific infinite series he is referring to can be assigned the value -1 as that is more usable than an infinite series. Don't claim he is wrong because you do not understand what he is talking about, the video was a clever way to introduce people to some things done in higher level math. The series can be infinity or -1.
xSandman16x 3 days ago
@goej42 You and all those upvoting you obviously don't understand the concept of infinity. Infinity+1 is still equal to infinity, so there is no "shift." What this video portrays is actually accurate, just like how .9999..... (repeating to infinity) is exactly equal to 1.
ManBMitt 3 days ago
@goej42 No, no, he's got it right. And wrong. You can use the same logic to say it equals infinity. (-1 + 1 + 1) = -1,-2,-3... + 1,2,3... +1,2,3... yields 1,2,3...
The problem is that "infinity" and "numbers" are different. What you said would apply to a finite series of numbers, but "infinity" is an abstract concept of numbers, which is weird because numbers themselves are abstract.
AltainiaInfinity 3 days ago 2
@goej42 2, 4, 8, 16, 32
-1, -2, -4, -8, -16
-1, 0, 0, 0, 0, 32 = 31
just as 1 + 2 + 4 + 8 + 16 also = 31
However, this is infinity. Both series of numbers stretches infinitely with no end, which is the "same end". It can be represented (though not defined) as 2, 4, 8, 16, 32... to the "same end"
-1, -2, -4, -8, -16, -32... to the "same end"
which all cancels out except '-1'.
Again, the ultimate issue here is infinity is not a number in the way we usually mean.
AltainiaInfinity 3 days ago
@AltainiaInfinity Google ratio test for a power series. It will prove that the series is divergent (the sum of the series is not a finite number)
goej42 3 days ago
@goej42 It's not wrong. Your reasoning is incorrect. Since there is no limit, there can be no extremely large number (infinity is not a number) and therefore this is still valid.
Racoonieboy 3 days ago
@Racoonieboy Use Ratio Test for sum of a power series to find that 2^n is divergent. It's Calculus II in any university course. Or google it.
goej42 3 days ago
@goej42 except since both series go to infinity there is not a finite very large number in the end of either. Basically the fact that the starting seiries is 1 step ahead matter only in the event that you have a difinitive end point. If you can not define the end member of the sequences you are left with just "-1".
zerocoldtm 2 days ago
@zerocoldtm yes, infinity breaks math :P I find that relieving as it makes me feel better about not being able to contemplate it either.
rich1051414 2 days ago
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@zerocoldtm "If you can not define the end member of the sequences you are left with just "-1"."
You are subtracting 1 from end member of the sequences you can not define, so it can't be equal to -1.
0001robm 1 day ago
@goej42 But we can add a 0 so that is is over -1 and 2 is now over 2.
MarkNie1 1 day ago in playlist MinutePhysics
That's wrong
AhMedRMaaty 4 days ago
OMG EVERY1 iz S0 smRt lol i wish i wus dat intelect. Does everyone have to reply with a paragraph? And it's a cute concept, but if you honestly feel the need to point out the fallacies that are apparent within, your dick is (2-1){1,2,4,8,16...} inches long.
HalfMileProdigy 4 days ago
Why did you FOIL the first parenthetical term? That can be completed, and according to PEMDAS, you do anything in Parentheses before anything else.
CBGB42 4 days ago
Infinity is just as 'weird' as Zero as far as I can tell. Infinity and Zero stay the same no matter what you do to them. There is no 'Half-Infinity' or 'Two-Infinity' just as there are no 'Half-zeroes' and 'Two-zeroes'. However, let's do some 'creative math': Infinity = (2 - 1) x Infinity? We can also write this as: Infinity = (2 x Infinity) - (1 x Infinity) ... Wait a Minute! 2 x Infinity is still Infinite thus Infinity! So, Infinity = Infinity - Infinity, so Infinity = 0? Infinity = -1 AND 0?
Zelalas 4 days ago in playlist MinutePhysics
@Zelalas Yes, that's what happens when infinite numbers are used as though they are the same kind of thing as integers or 'real' numbers. They are not. Compare, for example, saying Egg-Magnet=Despair, and concluding that magnet is a very weird number indeed. Rather, the operations you're using (+,-,*... as used with, say, integers) only have defined meaning with a very specific set of inputs. "Infinity" is not one of them, just as 'magnet' isn't, or 'the set of negative integers.'
dymaseran 4 days ago
@dymaseran Yes, but this video, in my eyes, treats them as such, Why? In the above case 2 numbers would remain after the cancellation process if infinitely positive numbes cancel out infinitely negative numbers by using 2-1 . -1 and the 'Highest number' which is, you guessed it, Infinitely large. Thus the answer would not be, -1 but - Infinity.
However, - Infinity does not really exist, as infinity is not a number. - Infinity is still Infinity as both are the same thing, just one is 'backwards'.
Zelalas 4 days ago
@Zelalas But there is no final number. That would be true in a finite sum but in an infinite sum all terms but the number 1 are present in the positive part. Unless you define a bound on the set of natural numbers there will always be a non infinite number - a non infinite number. The natural numbers don't suddenly become infinity. Unless you add exceptions to the distributive property of multiplication or the associative property of addition this video is mathematically consistent.
Raztheeccentric 4 days ago
@Raztheeccentric True, but this is the problem and why you cannot just say: 'I do this and voila! The sum is -1!'. As I stated before, try using 3-2. It doesn't work the same way anymore. Exceptions are already in place.
Also, it should say this: {2-1,4-2,8-4,16-8 ....}
The inherent problem here is that we shift one sum, the negative one, off by one number when we actually shouldn't do that, just so we can get the -1. This is only possible because Infinity is not a number you can reach.
Zelalas 4 days ago
@Zelalas Shouldn't isn't the same thing as "can't". You're right in that you "shouldn't" have an infinite sum of positive numbers equal to -1. In fact, it can be proven that using the addition operator on only positive numbers you can only get a number greater than any of the original numbers. Likewise, as you said using 3-2 you get a different answer, which "shouldn't" happen either.
But the method itself is not incorrect. The result is impossible despite of a correct method.
Raztheeccentric 4 days ago
@Raztheeccentric Okay, Got that. Thanks for the explaining. Really appreciate it =D
Zelalas 4 days ago
@dymaseran Also, 3 - 2 = 1, thus... {3,6,9,27,81....} cancels out with... {-2,-4,-8,-16...}! Wait a minute.... How come infinity now has a Infinite answers?
Also, If I got anything wrong, feel free to correct me! (I know you will, this is the Internet!)
Zelalas 4 days ago
@Zelalas Correction: {3,6,12, 24, 48... } I think you get the idea...
Zelalas 4 days ago
@Zelalas no. infinity - infinity is not 0, its undefined. Look up Hilbert's Hotel or watch To Infinity and Beyond - Horizon - BBC.
also infinity doesn't equal -1 either, the series 1+2+4+8+16+...+2^n does - if you use the Zeta function. That is what this video was trying to convey. The series 1+2+3+4+5+... n = -1/12 as n tends to infinity.
Math does not allow simple arithmetic like on divergent series, if you could you end up with the answer 2^n-1 where n tends to infinity.
0001robm 4 days ago
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Zelalas 4 days ago
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@0001robm Ah, my mistake. I was under the impression that. the series 1+2+4+8+16+.....+2^N had the answer: ( 2^(N+1))-1. Thus 2^N+1 would have to become 0 for this to work. So if 2^N+1 is Infinity and we need a 0 for this this work.....
Also, What happens if you try using 3-2 instead of 2-1, same results?
Zelalas 4 days ago
@Zelalas 2^n (where n is becoming infinitely large) is basically a large positive number. since n is infinitely large it doesn't matter if its n, n+1,n+1000 etc as its the largest natural number.
2^n -1, therefore is a large odd number.
0001robm 3 days ago
@Zelalas 1+2+4+8+... should also give a large odd number (if using basic arithmetic)
if this is allowed (an apparently its not) 3-2 will give the same result
btw first time i saw this video i wasn't really convinced either, but string theory etc are based on extremely complicated math that with divergent series.
Euler 400 years ago 'proved' the sum of natural numbers is -1/12.
if you go to wolframalpha com and put in 1+2+3+4+... and look at the regularized result
0001robm 3 days ago
I love this channel but I'm pretty sure that you cant cancel out like that.
TABLEstairs 4 days ago
I had to watch that twice to see exactly what he did there. That is crazy. I am utterly astounded and can't find a single argument to disprove that. Infinity really fucks with math sometimes.
GnarlyNewEngland 4 days ago
This is completely a wrong prove. I don't have time for these funny thing. Everyone should ignore this. Don't let it put you down.
noisauromeo 5 days ago
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TheBlinkyImp 5 days ago in playlist MinutePhysics
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TheBlinkyImp 5 days ago in playlist MinutePhysics
TheBlinkyImp 5 days ago in playlist MinutePhysics
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This would be correct IF ONLY THE NUMBERS HAD A LIMIT. When you multiply the (2-1) with the (1+2+4+8...) you should keep in mind that you multiply the 2 and -1 with the SAME AMOUNT OF NUMBERS but since they are infinite then when you get to
= 2+4+8+16
-1-2-4-8-16 you CANNOT cancel them out because as you can see there are 4 numbers in the upper row but 5 numbers in the bottom one. I hope you understood my point of view. However if I am wrong please point out my mistake.
J0nYJ0nY 5 days ago in playlist MinutePhysics
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J0nYJ0nY 5 days ago in playlist MinutePhysics
(2-1)( 1+2+.....) = 3+...
2*(1+2) + (-1*(1+2)) = 3
Since we are distributing to infinity, lets add to one side of the distribution at a time starting with the right side:
2*(1+2) + (-1*(1+2+4)) = -1
then add the 4 to the left side:
2*(1+2+4) + (-1*(1+2+4)) = 7
Same thing...
2*(1+2+4) + (-1*(1+2+4+8)) = -1
2*(1+2+4+8) + (-1*(1+2+4+8)) = 15
Keep doing this and you will see a fluctuation between -1 and the sum of the original pattern. Over time the average of the results will be -1.
bboylayz 5 days ago
@bboylayz So just to beat a dead horse: the point is, infinity doesn't have a speed or time, it exists forever so trying to distribute it at a set point in time doesn't quite make sense. But when thinking in terms of matching up equal but opposite numbers to cancel them out, there is always a matching number on the other side of the distribution in the world of infinity except for negative 1.
bboylayz 5 days ago
This actually does make sense when you are talking about infinity. Took me a second to realize he didn't use the same amount of numbers while distributing, and then it made sense. This was intentional, and the best way to think of it is that infinity has no last number. So as you keep going, every number in the pattern has (or EVENTUALLY WILL HAVE) an equal but negative value to cancel it out when distributing the 2 and -1 (in 2-1)... That is every number but -1.
bboylayz 5 days ago
"today a physicist does math"..... A PHYSICIST ALWAYS DOES MATH!
jizzo492 5 days ago
BODMAS bitch, do the brackets first...
(2-1)(1+2+4+8...)
=(1)(infinite)
=infinite.
31273127a 5 days ago
Nice video, but it overstates the actual result. In the usual sense, the summation is certainly infinite. The summation also behaves in some ways as the finite integer -1, and so there is some rationale for treating it as such. But, it is an overstatement to say that the summation equals -1. As @superkoopasirf suggested earlier, I also recommend googling '1+2+4+8 wiki'.
ig0ro 5 days ago
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0:26.
Why did he do -1 -2 -4 -8 -16 etc?
japanboogie 6 days ago
then again, is its 1+2+4+8+etc= (1)(1+2+4+8+etc.) wouldnt u have to do mukltiplication first? so that (1) is distribiuted and thus not a negative-1?
or woulldnt there also be a (2-1) on the other side of your equation? Basically a (2-1) on both sides of an equation thus cancelling out?
from what im geting from this, nothing equals itself and always can be traced back to and equal -1.
japanboogie 6 days ago
@japanboogie Let me try explaining: 1+2+4+8+etc... is nothing but (1)(1+2+4+8+etc) because we're basically multiplying the equation by one. Now this means we don't necessarily have to multiply the LHS by 1. Yeah?
Now, 1=2-1. Hence we can write the previous equation as: (2-1)(1+2+4+8+etc). Now simplifying the brackets: (2+4+8+etc.) - ( 1 -2-4-8-etc.) = -1.
Hope you got it. :)
srav953 6 days ago
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"Interesting, however, remember that infinity minus infinity is an indeterminate form.
This is what he is doing, that is why he got -1.
The sum 2 to the power of n is divergent because it is a geometric series with a ratio of 2 which is larger than 1.
Therefore it cannot have a sum."
- My Schurr High School AP Calculus teacher, who had a 100% pass rate in AP Calc BC in 2011
mrtsunny 6 days ago
This isn't correct because you didn't use the same amount of variables for both sides. It would actually look like this -
(2-1) * (1+2+4+8+16...)
2 + 4 + 8 + 16 + 32
- 1 - 2 - 4 - 8 - 16
which would equal
1 + 2 + 4 + 8 + 16.
You can't just add variables to one side of a Divergent Series and not the other.
FlareDraco 6 days ago
surely it's just n=n
TheLemonAlmighty 6 days ago
0:26.
Why did he do -1 -2 -4 -8 -16 etc?
Tamarrack 6 days ago
@Tamarrack im guessing he tried to make the left side equal 0 or something like that.
japanboogie 6 days ago
So what you're saying... Is that, there's -1 comments on this video?
TheRetna1111 1 week ago
I dont get it.
250666bmf 1 week ago
Try foiling it like you're sposta.
masonnf1 1 week ago
Nearly every comment is saying how this doesn't work. People need to understand there's more to mathematics than just the real numbers. Complex analysis, get to know.
ImJoeYeah 1 week ago
The problem with this Series is, you subtract "infinity" from "infinity" which not well defined. Your math is wrong.
aVoNgfx 1 week ago
In fact he used the equation of sum to infinity. S( ∞)=a/(1-r) where a is the first term of the sequence while r is the common ratio of the terms( 1/(1-2)=-1). However, this equation only applies under condition of -1<r<1. Obviously, 2 is out of range. Try to download "Graphmatica", a graph plotting software, and type"y=(1-(2^x))/(1-2)" , which is the equation of sum of geometric sequence ( S(n)= a(1-r^n)/(1-r))and hit enter. Sure you'll find that the graph keep increasing up to infinity.
imbcw 1 week ago
One day this guy is going to divide by zero and kill us all...
Toughcookie2134 1 week ago
@Toughcookie2134 People have been dividing by 0 for ages. Check out the Riemann sphere and extended complex plane.
ImJoeYeah 1 week ago
you shifted the negative values to the left which is deceptive, cus the -1 is still there, but then 32 would be on the top, giving a sum of 31 at the 5th term
FndASltn 1 week ago
Bullocks ...n may increase infinitely, but at any given value of n: 2^0+2^1+2^3+...+2^n=2^n-1
skoockum 1 week ago
You had me at "Math Ahead"
skoockum 1 week ago
Your math is bad and you should feel bad!
HaydenScheib 1 week ago
at 0:28 ALMOST everything cancels there is -1 but there is also a +2^inf that doesn't cancels out soits stil inf
hgeorgehful 1 week ago
@hgeorgehful No, that's simply not how it works. There is no 2^inf term. The sequence 1,2,4,8,16,... contains every term which the sequence 2,4,8,16... does, but also contains the additional term of 1. Trust me, I'm a masters student in math.
jelinlikeafelin 5 days ago
Well, ∞ Σ 2^x → ∞ n=1
...and very quickly so as a certain emperor found out when he lost all his rice. BUT, when mathematics starts to get fuzzy, interesting things happen. Don't loose faith in OMF ;)
Telliria 1 week ago
Mother of God
TurtleHunter29 1 week ago
lol I was thinking about this when I was in high school
darkilustrisimus 1 week ago
that's cheating
alden337 1 week ago
why do you have to substitute 1 with 2-1, you can also do that with 3-2, right?
stefanocts 1 week ago
@stefanocts But that would be bitchy to simplify.
AsianTaeHyun 1 week ago
@AsianTaeHyun yes, but wouldn't the answer be different?
stefanocts 1 week ago
Actually, Wikipedia does confirm he's not completely insane! According to the encyclopaedia, it really is negative one. Just Google '1+2+4+8 wiki' and you'll find the page.
superkoopasirf 1 week ago
If you want something nifty and actually correct, how's about the fact that 0.9999...=1. That's pretty cool when you prove it. 1=3*(1/3)=3*0.3333...=0.9999...
tFighterPilot 1 week ago
BUT you didn't cancel out all the pairs. unless you do that, you have to use limits.
pcdsgh 1 week ago in playlist MinutePhysics
The answer is not -1
Actually the answer is last term, that is, infinite term - (1)
You can understand this by considering only first few terms.
abhim7 1 week ago
he took ∞ and changed it into 2∞-1∞=∞-∞ which is an indeterminate form.
vee00Roar 1 week ago
There is just one thing I don't understand and would like an explination. How is he able to move the negative two over one so that -1 isn't subtracted from it? In other words, why doesn't he subtract -1 from 2? He instead moves the top equation over one position, why?
ideedkindsir 1 week ago
@ideedkindsir I agree with you. He uses visual similarity to position the numbers- it only LOOKS logical. Thus the fooling, because -1 should be actually under +2 as you stated.
jopantonio 1 week ago
@jopantonio All the people on here are over thinking it. It's wrong because he simply wrote the numbers wrong.
ideedkindsir 1 week ago
Yeah, -1, right. This could be a nice way to show it's more like 2^(n+1)-1, which is also really easy to show by induction. It really hurts to watch this.
mgx3141 1 week ago
He did not put a positive 1 at 0:27, so obviously when he cancels out everything else -1 will be the only term left over. What did positive 1 ever do to you, bro?
DoughyDoughBoi 1 week ago
@DoughyDoughBoi it's because when you expand (2-1) x (1+2+4+8....) 2 x 1=2, so there is no +1
LotsOVideos 1 week ago
@LotsOVideos You're right, I missed the distribution there. I will have a rebuttal at some point in the future.
DoughyDoughBoi 1 week ago
this is stupid...
you just assume there is no last term huh.... ya, forgot about that?
let me say it in a way you may understand.
... ( (∞-2) + ( ∞ -1) + (∞)) --- ((∞-1) + (∞))
let us simplify that down... oh look, we get ∞
happybobyou 1 week ago