Suppose you add up one plus two plus four
plus eight plus sixteen plus… well, you get the point. Each number is twice as big
as the previous one, so it’s pretty obvious that this sum is infinite… But wait a second! We can multiply the whole
thing by one and it’ll be the same, right? And one is the same as two minus one… so
we have two plus four plus eight plus sixteen etc., minus one minus two minus four minus
eight minus sixteen… So almost everything on the right side cancels,
and voila: 1+2+4+8+16, and so on, is negative one!

Author Since: Mar 11, 2019

  1. I think he's messing with you. The throwaway line "so almost everything on the right side cancels" is the point. The "almost" part that doesn't cancel is infinite (plus -1)!
    -1 + infinity – infinity does not equal -1, because infinity has no definable value.

  2. it would equal 2n-1, n being the number you stop at, which if it's infinity it would equal infinity minus 1

  3. "1*x=x FOR ALL X"
    Infinity isn't a number, therefore not even an x.
    If so, then:
    1) 1*infinity=infinity
    And because
    2) n*infinty=infinity FOR ALL N
    2+1) 1=n, FOR ALL N.

  4. The only thing he does wrong is the first series 2+4+6+8… has one number more than the series -1-2-3-4-5…which does not cancel and that number is infinitely large, so the sum is -1+infinity=infinity

  5. I thought that "speed" of numbers going to infinity is important and you changed it saying "it cancels out" but it doesn't because of different speed.

  6. I Dont know if this is true but i dont what to look it up 😛 But I do have a face like u and my face is pretty hot :^ )

  7. I don't like this kind of videos, because they make mathematicians seem like idiots. Without a little of explanation this video seems completely no sense.

  8. It's wrong…. Think only 4 numbers at a time….
    1+2+4+8 = 1*(1+2+4+8)
    =(2-1)*(1+2+4+8)
    =2+4+8+16
    -1-2-4-8
    =16-1
    =15…..

    Similarly for your theory….
    It should be ( infinity – 1)
    Am I right??
    Plz answer @minutephysics #minutephysics

  9. ok guys i will talk about this thing

    1+2+4+8+16+32+… is in fact -1 but this explanation isn't the right one

    https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF

    don't expect to understand 😛

  10. In 0.28 you add two infinite series think that there are n numbers in both series you leave -1 and add every thing and n-1 numbers become zero at last there is a number which is infinite but you didn't talk about it so the middle numbers cancel and only -1 and infinite is left so the answer is infinity-1 which is also infinity
    So sum of series is infinity

  11. Well if this is true then you could argue that it is equal to anything as (3-2) is also 1 so then the series equals -2 or -4 or -12 or -4000

  12. "Today, a physicist does math." I'm scared… 'scuse me, I have to go hide under my blanket. If you try to come after me, be warned, I have a flashlight. X3

  13. the same we could do with 1+2+3+4+5+… but that was already -1/12 so how could it be 1 in here? the answer is: infinity is weird

  14. Hey Henry I really appreciated this video but it isn't correct the answer would be (2^n-1)-1 where n is the last # but since the is no last # it would be infinite

  15. This is just like saying (infinity-1)-Infinity=-1, which is stupid. You can't actually subtract infinity from one another because it doesn't have a set value. It's infinite. Infinity can be 1+2+4+8… or 2+4+8+16….. And since infinity-infinity=infinity, then (2+4+8+16)-(1+2+4+8)…. will not be -1. It will = infinity

  16. bro this is wrong.the last number will be multiplied by 2 and the last no multipleed by 1 is subtracted by the before number multiplied by 2.

  17. Okay lets look at your problem and answer,
    (2-1)(infinte no.s)
    That would be,
    2*(infinte) -1*(infinte)
    Making it,
    Infinte-infinte
    Which is classified as undefined by the math community.

  18. Hey, this is not how infinite sums work. You have to calculate lim (sum 1 to N) – which still is +infinite. The '…' can't be used like that unless you have something at both ends

  19. Ok… but how can a sum of infinite positives become a negative number?
    Where does this number come from?
    This should be a paradox!
    The infinity with the negative numbers is one digit "longer" than the one with the positive ones since if we try this with a set amount of numbers the negatives will be one number short of completely cancelling out the positives, but here this can not be because both sets are infinities!

  20. I think this is a part of reinmann hypothesis…….i.e there are some series whose sum are not independent of the arrangement….
    i.e there are some series for which u can't write (1+2)=(2+1)….that sort of….

  21. If you start adding from 2, should it be 2-1+4-2+8-4 instead of this: 0:27? (he writes -2 under 2 and -1 under nothing)

  22. Hello everyone, i found three mistakes till now in videos under this title (minute physics) the FIRST
    is about twin paradox in the special theory of relativity as they dealt with a frame forgetting about the other in the specetime diagram

    SECOND
    in (hitting the sun is hard) as the speed of 11.2km/s is never the speed to escape from earth's gravity as physicists think or from the solar system as the video publisher says
    as when (mv^2)/r = GmM/r^2 and so v^2=GM/r when gravity is equal to the so-called centrifugal force the object is balanced yes, but remember that when (mv^2)/r = GmM/r^2 then multiply both sides by r/2 to get that
    KE=ABS(1/2(PE)) which means that you have only cancelled half the gravitational earth's potential energy using your KE in a trial to be free, so you need the double of this KE to escape completely from the earth's gravitational field and have a total energy of zero as when the orbit is getting larger and the object is moving away from earth the gravity deos it's negative work to leave the object with less and less KE for it's total energy to be then 1/2(GMm/r) as r is the radius of earth in the previous explanation

    THIRD

    in this video, when you add up the numbers, let's say you add the first 60 terms then
    1+2+4+8+16+32+64+128+…++..++.+.+A as A is the 60th term then
    (2-1)(1+2+4+8+16+32+64+128+…++…+++…A)=
    2+4+8+16+64+128+256++++++++…++A+2A -1-2-4-8-16-32-64-128-..-..-..-..-A = 2A-1= 2A approximately
    another proof:
    2^0+2^1+2^2+2^3+2^4+2^5++…++…++2^n as nis veeeeery large number =???

    take 2^n as a common factor then:
    2^0+2^1+2^2+2^3+2^4+2^5++…++…++2^n =
    2^n [[1+1/2+1/4+1/8+1/16+..++…++…++….++1/2^n]] = 2^n [[1/(1-2)]] = 2*(2^n) as 2^n here is like A in the previous explanation

    so never think that all the terms cancel
    as whatever number of terms you take the last one multiplied by two does never cancel and so

    1+2+4+8+16+32+64+128+256+512+1024++..++..++..++..G = 2G as G is very far away term

    so never be tricked it's sooooo silly

  23. This is Ramanujan's sums, just like e.g. 1+2+3+4+…=-1/12.

    Mathematicians are skeptical about them, but they're (sums, not mathematicians) commonly used in the string theory. WHY!? Quantum mechanics!

  24. Lets take an example of finite series…

    1+2+4+8+16+32=63

    (2-1)×(1+2+4+8+16+32)=(2+4+8+16+32+64)-(1+2+4+8+16+32)
    =126-63
    =63

  25. For everyone saying its wrong
    1+2+4+8…x2=2+4+8+16…
    1+2+4+8+16
    2+4+8+16
    Look, it is the same as taking away 1 and
    -1×2 =-1-1
    1+2+4+8=-1

  26. If anyone is curious, rearranging a summation is only allowed if the series is absolutely convergent. If you rearrange something that is divergent to infinity then you can create any number you wish. This type of thing can be learned in an undergraduate real analysis course in college.

  27. No! You moved them by one digit.
    It’s 2-1+4-2+8-4+16-8+32-16
    = 1+2+4+8+16
    The same thing!
    Instead of 2-2+4-4…
    If you do it that way you’ll obtain “the last positive number” -1 not just -1

  28. Hey, I know that this is a common calculation, but in my opinion there is a fault.
    If you do so, you are only calculating to a finite number. In your example it is 8. But later you use the 16 becasue 2*8 = 16. But you are also counting to 16 on the negative side where 1*16 = 16, but you are counting one level higher on the negative side.
    So, as long as you keep on counting only up to a finite number, you will also do this fault. If you don't, the highest positive numbre is twice the highest negative number. So if your highest number is called n, your result is 2*n-1.
    So, the higher you count, the higher is your result.
    The result for n = infinite is 2*infinite – 1 = infinite.
    You can only get a finite answer if you do the fault to count one level higher on the negative side that on the positive side.

  29. voila my ass
    did you forget that somewhere along your infinite series you have a bloody infinity that just don't happen to cancel out

  30. You don't write a series like this if you're doing calculation on it. The series is 1+2+4+8+…+n
    Hence the result ≠ -1 but 2n-1

    Happy calculations! 🙂

  31. this might explain it
    https://docs.google.com/document/d/1y2NAIxo_EfeSZ8UKBiraAtjz8Gkbyu_VwJrCEWjTEns/edit?usp=sharing

  32. You made a good effort to fool people who are weak in maths but it was not enough for people who are crazy about mathematic

  33. Actually, to do algebraic operations on a sum, it is necessary to show that the sum converges. So this proof is wrong, because this particular infinite series is divergent.

  34. I don’t see a problem with this.

    Jk

    If he were to do the opposite, distribute the 2-1 instead of the infinite series, he would’ve gotten back to the infinite series.

    And that’s why it’s wrong.

  35. Don't confuse others' concepts of mathematics. The p in the (1-p)+p=1 equation must be between 0 and 1, then your method is correct.
    if p=2 and the last number is 8 (equal to power(2, 3)), then follow your solution that (2-1)(1+2+4+8) = 2+4+8+16 – 1 – 2 – 4 – 8 = 16 – 1 =power(2, 4) -1
    So. if 0<p<1 then the equation 1+power(p,1)+power(p,2)+…. = 1 / (1-p)
    if p>1 then sum of the equation is power(2, n+1) – 1

  36. Neeeh. If u stake a cretain number instead of infinity,suppose u stop at (1+2+4+8+16) then ypu will get the 15 =15

  37. A man gives you 1 dollar then 2 dollars then 4 dollars then 8 dollars and so on for the rest of eternity ,but he secretly ended up stealing 1 dollar from you.

  38. This is non sense math cause you first do equations which are inside the brackets. So in the bracket one is always 1, in the second it's always infinity which makes statement always true and him and idiot.

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