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Thomas
@aviationdoctor.eth
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)
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Alberto Ornaghi
@alor
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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Thomas
@aviationdoctor.eth
(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?)
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Alberto Ornaghi
@alor
a divergent series does not have a define sum. the result is simply "undefined".
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Thomas
@aviationdoctor.eth
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...)
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