Numberphile v. Math: the truth about 1+2+3+...=-1/12

It makes no sense, because we don't know the true nature of our Universe which is dual. 👾

Numberphile must have had a "buffer overflow" to reach that result...

When numberturd did that video, I unsubbed.

The worst thing about this is I was introduced to this fallacious sum in a stanford lecture on physics. It's apparently the basis of supersymmetry.

Numberphile prof teaching p-series with an=(1)^-n = div. And then doing this video lmao

Me who knows 1+2+3=6

Hey - you changed t-shirts five and a half minutes in.

I would be very happy if someone gave me 1+2+3+....$ and I had to give him -1/12 $ back!

This video is so therapeutic after seeing that Numberphile video.

hahhaaaaaaaa

Most functions we're familiar with are analytic functions, but most functions are not analytic functions. An analytic function roughly corresponds to a function from the natural numbers to the real numbers which encodes the coefficients of the infinite polynomial. There are only continuum many such functions (i.e. there's one for every real number). However, the number of functions from the real numbers to the real numbers is more than this (one for every subset of the real numbers), infinitely many more. In other words, if you were to generate a random function from the set of all possible real to real functions, the probability of it being an analytic function is 0, for the same reason that generating a random real number has probability 0 of giving you an integer, just one level of infinity higher.

but it was 1-2+3-4 .....

I love Mathologer. But I can't like this video.

Imagine flipping a switch infinite times and your lightbulb is just half on

The thing about maths is that mathematians always care about and give the general case
whereas physicists in physics always cares about and give the special case

And yes Richard Feynman said something like this

But modern physicists don't believe they have to follow all these rules. For example, they have this little procedure called "renormalization," in which they assert that the result of infinity minus infinity is an empirically observed finite quantity. And this seems to serve them just fine.

Where do you get your T-Shirts!!!!!!!!!!

for supersums, what if we need an infinite amount of averaging but after that actually converge to a finite number? (would that be even possible?)
does that sequence then still have a supersum? thx!

exactly. as soon as i just saw "taking the average" of 0 and 1 becomes 1/2 i just started laughing and knew that it's just sort of a joke.... just because it's infinity you can't just take an average out randomly with the 2 possible "answers" which is 0 and 1

Today I've learned that for english speakers series are either "convergent" or "divergent" (unless I'm missing something and I would be grateful for any input about that).

In italian "convergent" is the same, but "divergent" is used only when limit is either + or - infinite, the third category is called "Indeterminate", and it's when the limit does not exists, which is the case of +1-1+1....

Thank god for this. I immediately found their conclusion ridiculous. Never send a physicist to do a mathematicians job :)

Respect for ramanujan sir

It's funny that this video got recomended to me because just yesterday I finished the other video and was really confused about them shifting the 1 - 2 + 3 - 4 + 5... term over by one and subtracting it from the 1 - 1 + 1 - 1 + 1... term.

That's usially a big no no in math because you can make any infinite sum equal whatever you want if you do that.

What's (1 - 1 + 1....) + (1 - 1 + 1...)?

According to the other video's logic it could be infinity since you can start by adding the +1 values of the first set to the -1 values of the second and see that there's a 'one to one' correlation.

Then the equation could be rewritten as 1 + 1 + 1... Which is nonsensical.

You could also use that same logic to show that it's any other value if you really want to.

Awesome video!

If this is not true then why do so many people deem this answer to be so important and for all intensive purposes correct?

Ramanujan summation of divergent series

I love the deranged giggle

Thank god someone is policing the math Internet!

While it is wonderful that these are so thought-out and then scripted, you take away from that drastically when you mouth the lines of the sidekick as he speaks them.

THANK YOU! The -1/12 meme has gone way too far.

This is the real East Coast vs West Coast thang.

This was like one of the first things they covered in undergrad, the series that alternates positive and negative 1 they told us to think about as a digital switch, it's either on (1) or it's off (0) and it can always be made to be in one of those states by adding an extra term but it can never behave like an analogue switch and be in a state that is some measure of two values it takes. Really helped me to understand why its sum cannot be assigned a value. This video made more clear outside of thay intuition.

I knew it!!! I thought I was going crazy!!! It turned out I was right!!!

Jesus christ it is...

Analytic continuation is completely determined, provided some conditions are met. The new domain must be specified, it must be a connected open set, and an extension must exist. For example, the logarithm cannot be complex-analytically continued to the complex plane, even after you throw out the obvious singularity at 0. You need a branch cut from 0 to complex (unsigned) infinity, and the values depend on how you choose the branch cut.

Yes, thanks to Mathologer for exposing Numerphile. It is shocking and sad that Eddie also fell prey for Numberphile.

Doggon Scathing!

It's not supposed to be rigorous but is not incorrect either. What they did was to put a value on a DIVERGENT series and go on from there. They didn't explicity said that they were doing a Ramanujan Summation. The first series on numberphile video is divergent because is undetermined at infinite (neither 0 or 1), but they assigned 1/2. The rest follows and is correct. You assumed convergent series, that's another beast altogether.

Since every number can be written as the sum of 1’s:
1 + 2 + 3 + … =
1 + (1 + 1) + (1 + 1 + 1) + … = -1/12

Correct?

Numberphile is a great example of PhD's run a muck. This claim is one of the reasons I quit watching them.

All economic wealth would be worthless according to -1/12 theory.

I love the T-shirt change to express the toppics.

well thanks for clarifying, I was about to use that addition to pay a debt and get 1/12 of the debt in return

What you do do is fals but isn't the same S

Thank you for this video!

in the last part, we can also say eta is analytic for z>1 since (zeta(z))[1-2/2^z] is analytic for z>1. Doesn't this equality `contradicts` itself if we re-arrange (1-2/2^z) "right-to-left" to "left-to-right". And also why eta(-1) is assumed to be equal to S2(=1/4)?

It is funny to me how mathematicians and physicists approach maths differently. For the physicist, nature is the object of study, and maths is a tool. The occurrence of an infinite sum en route to an answer which you know exists is not a reason to give up lest you "break the rules". But for the mathematician, the rules themselves are the object of study, and violating them quite rightly invalidates the enterprise.

Regardless, I think Numberphile were not presenting their basic summation proof as to be taken entirely rigorously. The sums they wrote down are confirmatory of more rigorous methods they kept referring to.

This feels like the history of i.

Team Numberphile
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