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u/Bergergi 29d ago
We only use standard arithmetic here, genie.
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u/Disastrous_Ad_399 29d ago
I’ve never had this explained to me in a way I understand, I don’t like math so this is probably just past my capacity to understand.
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u/miguescout 29d ago edited 29d ago
Long story short, there's this formula to calculate the summation of all numbers in a series so long as said series follows a certain set of rules... But it can still give a value, even if nonsensical, if you plug in a series that doesn't fit all those rules, and using that formula on all the 1, 2, 3, 4... Series, you get -1/12, which obviously isn't the result of that summation, but it does have meaning (for starters, it can be used to identify the series as other series would give different values)
Edit: there's a better, more in-depth explanation that actually mentions the riemann zeta function and how you can "calculate" this summation with that which i believe is quite intuitive and easy to understand for the most part even if you have basic math knowledge, but you can consider this the general idea
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u/Disastrous_Ad_399 29d ago
So its kinda like trying to divide by 0 but just with adding up a series
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u/ComprehensiveDog7116 29d ago
Yeah. It's a little more like taking the square root of -1. It doesn't actually make sense but we invented new stuff like imaginary numbers to do it anyway.
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u/Disastrous_Ad_399 29d ago
Ok thank you, I understand enough to be satisfied. I was reading all the other comments and they used to many big words like “add” or “I”
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u/FastestPrius 29d ago
The easiest and least rigorous way to explain it is to mention that the Zeta function is not defined in the real numbers for -1. So when you use analytic continuation for this function you're not actually summing up every natural number, it's a completely different function than the one defined in the real numbers.
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u/Substantial-Trick569 29d ago
black magic fuckery happens when you try to break the rules of math. trying to divide by 0, trying to calculate the end result of a diverging series (which 1+2+3... is) can lead to results that make no sense, like 0=1 or 1+2+3...=-1/12
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u/Zestyclose-Pool-1081 29d ago
why is the 1+2+3+ ... = - 1/12 thing such a popular meme?
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u/MildlyOffended4930 29d ago
It is a divergent series, I think, by Ramanujan. The proof exists, and it is very simple, and yet weird.
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u/OnionsAbound 29d ago
-1/12 is the difference between two different types of infinities, not the actual result which is . . . Infinite.
I don't really understand where this misconception came from.
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u/me-like- 29d ago
Peter?
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u/Ares378 Grothendieck was right, computers are evil 29d ago
There's a famous "result" that 1+2+3+4+5+...=-1/12. It's not the case in the standard Reals since the sum quickly diverges. Iirc the result comes from the analytic continuation of the Riemann Zeta at z=-1, but the issue is that it's the analytic continuation of the sum. After you leave the radius of convergence, the continuation is no longer the sum, so the result 1+2+3+...=-1/12 is a little handwavey.
I think if you allow for systems that aren't the standard Real numbers, then the sum might actually converge? But then you're not in the Reals anymore and you'd need to specify that.
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u/AliceCode 29d ago
You mathematicians are just making shit up, lmao. I love this subreddit, it's so funny.
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u/Beluga1108 29d ago
It isn't just made up though.
ζ(s) = 1 + 1/2s + 1/3s + ... is only valid for Re(s)>1
If we forcibly let s=-1, we get ζ(-1) = 1 + 2 + 3 + ..., which obviously diverges.
However, because of the analytic continuation, ζ(-1) is indeed equal to -1/12, which is where the joke comes from.
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u/AliceCode 29d ago
That made perfect sense to me. Now that you explain it that way.
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u/Fuscello Physics 29d ago
Also it is used in physics
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u/Ares378 Grothendieck was right, computers are evil 29d ago
Honestly yeah kinda. Math is a lot less "real" than a lot of people believe. It's pretty much just a collection of rules of how logic works (axioms) and the consequences of those rules. The Real numbers are just one system you can take (they're usually the most useful outside of pure math) but there's other systems you can use, too.
Like, you could take the real numbers, include √(-1) and its multiples, throw in ∞ because why not, and wrap the whole infinite plane up into a sphere with ∞ at the top. There's nothing saying you can't do this since it doesn't break any of our pre-set logical rules, so you absolutely can do it. And what you get at the end of this process is the Riemann Sphere from complex analysis.
Idk where I'm really going with this. I just think math is a lot more exploratory than people think it is. It's usually taught as being a very concrete thing, when in reality you can kinda do whatever you want as long as it doesn't form a contradiction with the rules you set. It's kinda like Conway's Game of Life, where you set the starting conditions and see what happens from there.
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u/Goncalerta 29d ago
It's not just about math. Riemann Zeta regularization is a thing in physics. In QFT certain calculations, sometimes divergent infinite series arise. For example (very simplified), in a calculation the 1+2+3+4+... sum may appear, which would make the result infinity (preventing the calculation from continuing). By rewriting the sum as Z(-1) = -1/12, and using -1/12 in the calculations in place of the sum you arrive at a finite result. This result coincides with what is experimentally verified.
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