You're probably gonna hate this, but I think it actually matters how you add them up. Cuz think if you add 0 + 1 + 2 - 1 + 3 - 2 + 4... that pattern will always be positive. (And this is assuming we're only using integers)

[–] FooBarrington@lemmy.world 5 points 2 days ago

And this is why I don't ask the mathematicians in my life to sum up infinite lists of integers anymore. Smh

[–] voldage@lemmy.world 1 points 2 days ago (2 children)

Technically (not really) sum of all positive integers results in -1/12, which is due to the nature of infinite series and MATH I no longer understand. So it stands to reason, that if you add a -1 multiplier and sum results of both series together, you would get 0! Approximately.

[–] HeurtisticAlgorithm9@feddit.uk 1 points 1 day ago (1 children)

I also can't remember the maths, but iirc the -1/12 value is based on a faulty assumption somewhere in the calculation (probably dividing by 0 at some point)

[–] voldage@lemmy.world 2 points 1 day ago

The faulty assumption in the more naive approach was treating operations on infinite series in the same way you would treat operations on finite sums. The order of elements being added is important, as it does change the series, and the naive approach based on putting 0 in between each numbers like 0 + 1 + 0 + 2 + ... which was incorrect. There are ways to prove it does sum up to -1/12 from what I remember though, it's just the addition of 0's that's bad.

[–] TechieDamien@lemmy.ml 3 points 2 days ago

But 0! is 1.