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)

PhD in aviation ∩ climate science | Aviator, diver, ETH maxi, nexialist | Host of /diving /ethfinance /eth-staker /geopolitics /science /singapore /thomas

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.

(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?)

It's perfectly fine to say that a divergent series tends to infinity, infinite sums are just limits of partial sums.

But there is a very real and formal way in which a divergent series can be made to converge, and there are several methods for doing so (incl. analytical continuation, or the simpler regularization method shown in the last video that I linked). And -1/12 is a valid result, no matter how counter-intuitive (there's nothing intuitive ever about infinities anyway...)

a divergent series does not have a define sum. the result is simply "undefined".