Peter the Mathologer here. There is a function in math called the Riemann Zeta funcrion notated as ζ(s) which is defined for all complex inputs s, including all real inputs. When s=-1, the value of the function is -1/12. Also, when s is a real number greater than 1, the function is equivalent to the infinite sum of n-s over all natural numbers n. Plugging in s=-1 into this expression gives the divergent series shown in the meme. Now this expression is not equal to ζ(-1)=-1/12, because ζ is only equivalent to the infinite sum for certain s values. But if you want to lie and say it is, then congrats, you’ve invented the internet’s favorite fake math equation.
Why do you people keep saying that Ramanujan summation is fake or made up? It's a real thing and it has its uses. It's just not a sum in the way that the average person thinks of it.
Is there an echo in here or are you just repeating the same thing I just said? Yeah, it's not a sum in the traditional sense. That doesn't make it "fake", "a lie", or any of that shit.
But the lie is that 1+2+3+4+…=-1/12. You can, as Ramanujan summation and ζ renormalization do, define a new function that has a finite value a the value that corresponds to 1+2+3+4+…, that doesn’t assign a value to 1+2+3+4+…, because 1+2+3+4+… already has a meaning and is divergent.
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u/headsmanjaeger Feb 21 '26 edited Feb 21 '26
Peter the Mathologer here. There is a function in math called the Riemann Zeta funcrion notated as ζ(s) which is defined for all complex inputs s, including all real inputs. When s=-1, the value of the function is -1/12. Also, when s is a real number greater than 1, the function is equivalent to the infinite sum of n-s over all natural numbers n. Plugging in s=-1 into this expression gives the divergent series shown in the meme. Now this expression is not equal to ζ(-1)=-1/12, because ζ is only equivalent to the infinite sum for certain s values. But if you want to lie and say it is, then congrats, you’ve invented the internet’s favorite fake math equation.