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)
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.
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)
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.
Wait… If you add all the numbers together, don’t you get 0? Since for every number you’re also adding the negative.
Huh that would make him the most truthful politician… What a paradox
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)
And this is why I don’t ask the mathematicians in my life to sum up infinite lists of integers anymore. Smh
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.
But 0! is 1.
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)
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.