This Result Keeps Me Up At Night

What is the sum of all the natural numbers?! Of course the answer is obvious...right? Many have actually pointed to the result that the sum of natural numbers is negative 1/12 !

We're going to do a 1+2+3+...=-1/12 proof , then a false sum of all natural numbers proof. What can we make of this?!

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

1+2+3+4+5+6+n=-1/12 proof

#math #brithemathguy #sumofallnaturalnumbers

[erikm]

Average complex math theory fan vs. Average "It clearly isn't, just look at it" enjoyer

[MaxxTosh]

I’m so happy with the context you provided and ended on “no the sum of all natural numbers is not -1/12.” Too many mathtubers don’t do that!

[sheldonj.plankton]

Subtracting Infinity is not a valid operation, so everytime you subtract S you rule out that S could be infinity

[Konzon]

The problem isn't using the distributive law, it's grouping the series so that you are changing the "speed" at which the series grows.

[Snoozeforminutes]

Thanks to Ramanujan for giving us this wonderful series

[kodirovsshik]

This is the best explanation of this phenomenon I've ever seen and probably will ever see. Great job

[kasuha]

The main catch is assuming A is a number. While all the rules work for convergent series, in this case if we calculate A - A = 1 - (1 - 1) + (1 - 1) - (1 - 1) + (1 - 1) (with similar shift as we did with B), we get 0 = 1 and we just broke the math.

[GlorifiedTruth]

Brian, this is probably my favorite video you've done. Outstanding, clear explanations. When Numberphile made a video on this result, I commented that it was at odds with what I'd learned in real analysis, and the other commenters chimed in with, "I can't believe your arrogance, contradicting the work of high-level mathematicians." Well, the professors at UW Madison ARE high-level mathematicians! Thanks for showing the elasticity of this approach to computing divergent infinite... just super fun and informative.

[facttectsmart]

It was founded by great mathematician Ramanujan

[NGL_Shinhok]

1:47
The only logical argument is when you're doing the cheap trick of moving B to the right by 1 digit, you're agreeing that right now Im adding the 1 to the -2, the +3 to the -2 and at the end of the string I will come back and add the last remaining digit of the lower B to the first 1 of upper B.
But since the string never ends you're never doing that despite it being a requirement, it can't be ignored just because the string is infinite. You CAN NOT leave the 1 like that, because some day you'd have to add something to the 1 but you're never doing that and saying hey it keeps on forever!

So B ≠ 1/4
No.

[MasterHigure]

So glad to see a video about -1/12 that doesn't just stop at -1/12, but keeps going and demonstrates that no, it is not indisputably the case that the sum of all the natural numbers is -1/12. Yes, the series of natural numbers is closely linked to -1/12, but the conventional sum is not that connection.

[dukenukem]

When I do my taxes later this week, I am going to use the analytic extension of my gross annual income to assess my tax burden.

[dqrksun]

Thanks for putting a smile on my face for showing the Riemann functional equation 😊

[RedRing-tech]

Just found this video, and you instantly got a subscription from me. This irks me so much, and you succinctly described why and gave me a good counter example why it's flawed. Thank you.

[Infernal]

I am pointing at the culprit as being the "shifting the infinite series" and then adding them to infinity.
And that's because at any step, you are counting 1 element of the first infinite series while completely disregarding the same order element of the other infinite series, which the further out you are, the bigger that number gets.

[beketyermek]

Brian, youre the best! Thanks for the video😍

[absence]

The ruleset is sometimes not as unclear as presented here, both diverging and alternating sums don't have a general sum that can be simplified without implementing supersums or regarding a generalized function, e.g. Riemann-Zeta. Thereby neither shifting a sum "left" or "right" completely breaks the initial result, nor can the distributive law be utilized for an infinite sum whose identity isn't convergent. Just wanted to slightly highlight it more, bc if we were to allow all forms of algebraic operations on infinite sums, then we'd not only get proofs for -1 = 1 or N = R, but also break mathematical operations by applying mathematical operations.

The scorn of the goddess of infinity is eternal, infinite even.

[dorian]

Ramanujan summation is a beautiful tool, anytime I see -1/12 I can't help but think about it

[peckychicken]

I love how he explains this to us like we understand right away

[adityarawat]

For people who want to know, this is also called the Ramanujan Paradox