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.
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
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 read that and am now more confused. Thanks!
One of those cases where “first you learn the rules. Then you can learn how to break them.”
Fr I didn’t know what I was doing and tried it … broke both of my legs and gave me a concussion.
Don’t mess around with -1/12!
Consequences!
This is how you make a black hole isn’t it?
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.
That’s not how infinity works
Except it is. Infinities can have different sizes, and the size of an infinity needs to be taken into account when working with them.
Rama subtracted one infinity that is twice the size of another from it, so he subtracted twice as many numbers as his equation implies.
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.
Not when you’re adding them together.
c - 4c = -3 - 6 - 9 - 12…
In order to make c the same as the divergent series you have to subtract the series:
f = 0 + 4 + 0 + 8 …
Which is not the same series as 4c.
Why not? How does that change the value?
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.
You’re adding a bunch of zeroes. Zero is the additive identity. It doesn’t change the value.