ASTOUNDING: The Sum of All Natural Numbers = -1/12 [Science Video]


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The sum of all natural numbers (from 1 to infinity) produces an “astounding” result.

If you want to read more about this, Wikipedia also has an interesting article about the subject.

[Numberphile]





7 Responses to ASTOUNDING: The Sum of All Natural Numbers = -1/12 [Science Video]

  1. Only after doing some number gimmicking and using negative numbers and such. Yes, the mathematicians ‘show’ it to be true, but i will hold on to my disbelief of it. Especially since they are talking about infinities, yet ignoring them at the same time.

    • Yeah scientists show the effect of vaccines and climate change to be true as well but let’s hold onto our disbelief and trust in a god of our choosing.

  2. if they need to move the set of numbers in s2 and manipulate the others to get that answer then its just creating a branch of math in the same manner all other forms of math and math its self have been created, by observing something and applying an idea and name to it.

  3. I still just can’t figure out what law of math allows you to add two identical number lines together, while moving one over a place. What’s to stop you from moving it over a second place (or not moving it at all), therefore creating a new answer to 2Ssub2. Because you are still considering the two number lines to be the same, this new answer to 2Ssub2 is still usable in the overall equation, thus giving you a different answer from -1/12.

    NOTE: I did not go and see what answer you get for moving over two places, or three, or what-have-you. If it just so happens that all answers are the same, no matter how far you move them, then why move them at all?

    • Matt, this proof is basically for laymen like us, if you want a more solid proof look at the other video.

  4. Take 2.

    When you sum sequences, you can’t just pair off numbers willy nilly. You have to account for all of them. That means you have to look at both ends of the sequence. If we take the sequence to k terms, then the sum is given by: 2 * S2 = {S2[1]} + {sum over (1,k] of (S2[k-1] + S2[k])} + {S2[k]} = {sum over [1,k] of S1} + {S2[k]}. It doesn’t matter what the first part sums to (0, 1, or if you prefer 1/2), because as k tends to infinity S2[k] also tends to infinity, positive or negative. S minus S2 is therefore infinity minus infinity which could be anything. In fact, in the formula S – S2 = 4 * S, if S2 is infinite, S must also be infinite.