A very wrong proof once showed that the sum of all positive integers (1 + 2 + 3 + 4…) was -1/12. In reality, the infinite sum has no solution, so this proof became something of a meme.
Technically technically, in some number fields (not the natural numbers) it is correct, but since it doesn’t apply to all number systems it’s incorrect to say it’s the answer without also specifying you’re using a nonstandard number system.
As someone else said, it’s used in quantum physics where a lot of fancy math is used in complex number fields.
TL;DR: in some interpretations, 1 + 2 + 3 + … equals to -1/12. This interpretation has actually found some uses in physics. In general, this is not widely accepted as it depends on a specialized meaning of the equals sign. It shouldn’t be used unless you really know what you’re doing.
I don’t like the Ramanujan explanation at all because c - 4c doesn’t equal the divergent series, since 4c is only supposed to subtract from every other number, so it has more terms at every single limit of n, and thus more terms at infinity. So c - 4c is just -3c, not a divergent series.
Infinities do have different sizes, yes. But not on that scale. Both of these are countably infinite sets.
Think about this: there are infinitely many primes. Obviously, not every number is prime. But you can still map primes 1:1 with the natural numbers. They’re both the same size of infinity.
It makes the series equal length. You’ll notice this is discussed in the wikipedia article, and a bunch of bullshit handwaving has to be done to try and correct for it.
c - 4c = -3 - 6 - 9 - 12…
Simple as that, not some crap divergent series. Rama was a troll.
To clarify you cannot add zeros to a non-convergent series, which the series c is.
In regular summation you are only allowed to add one zero to the start of a convergent series without changing it’s value, since you know a convergent series has a specific answer.
But for non-convergent series you cannot do this mathematically in normal summation.
The value of a series is calculated by summing to n digits, and extrapolating. So c to 4 digits is 10, and to 5 digits is 15. 4c to 4 digits is 40, and to 5 digits is 60. But the series 4c with added zeroes at 4 digits is 12, and at 5 digits is still 12.
So 4c and 4c plus zeroes are not the same series. The only way to make 4c work in the posted equation is to use “super summation” which is a load of bull. Someone else posted a good video showing why this is the case.
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