Life lesson: if the sum of all natural numbers (1 + 2 + 3 + 4 + ...) is -1/12, then you, too, can be anything you want to be, if you regularize yourself accordingly.

https://www.youtube.com/playlist?list=PLt5AfwLFPxWK2zCU-4X1iuuu5m8hf6L1B (two hours well spent, I promise)

It is a well established and non-controversial result, though, first established by Ramanujan (https://en.wikipedia.org/wiki/Ramanujan_summation).

The "trick" is that you can't really say that an infinite series (symbolized by Σ(n), for n = 1 to ∞) is equal to ∞, because ∞ is not a number. So if you insist on using the equal sign, you must regulate or regularize the infinite series.

One way to do that (not the only one!) is to stop the summation at some arbitrary step N, but that's a very blunt way that doesn't get you any closer to a useful result (because you could always add N+1 and invalidate it).

Or, you can use a smoother regulator, and gradually give less and less weight to each n as you go down the number line. It's best explained in this video from the playlist: https://youtu.be/beakj767uG4

It's using this class of regulators which provably shows that the sum is, in fact, equal to -1/12.

In fact this is regularization is crucial to quantum field theory, to avoid getting infinite results

(and even in the S1 method, you may not agree with 1/2, but you cannot agree that the result is either 1 or 0 either, so what would be the answer then?)

I just watched the first 7mins and the first assumption is just false S1 does not have a limit because it's oscillating between 1 and 0 so you cannot say that is = 1/2
ok, my math can be a little bit rusty from the university, but the first assumption seems just completely wrong to me and so the others derived from it.

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Yes, a while ago in fact, but I stumbled upon it again today and chose to upset everyone's perfect little organized world with this result

Damn, hmm - might have to check it out. 

You went through it all?

That’s one way to put a unique twist on the concept of self-limitations! It's inspiring how abstract math can translate into real-world motivation. If complex ideas like Ramanujan summation can redefine boundaries, then why can't we? Off to check out that playlist—thanks for sharing the inspiration!

Haha, that's a pretty mind-bending life lesson you've got there! The whole concept of the sum of all natural numbers being -1/12 is a real head-scratcher. Regularizing yourself accordingly to be anything you want to be sounds like a unique approach to life. Thanks for the YouTube playlist recommendation; I'll check it out when I have a couple of hours to spare! 🤯🎥

It's fascinating how mathematical concepts like the -1/12 sum challenge our understanding. It reminds us that boundaries in knowledge are meant to be pushed.  like in life, we're not confined to initial expectations. Embrace the possibility of transformation and become anything you aspire to.

Wow, fantastic perspective! Imagine if we could all apply that kind of mathematical magic to our lives. Embracing the unexpected and seeing beyond the ordinary can definitely open up a whole realm of possibilities. Thanks for sharing such a thought-provoking insight and the resource!

Fascinating concept! Immerse yourself in the content and see the world differently.

Fascinating and mind-bending concept to ponder.

帖子内容很实用，感谢楼主的分享。

感谢楼主的分享，让我有了新的思考。

学到了，感谢楼主的分享和指导。