hey guys... guys listen...
guys, wait, listen....
if you.... hey, listen...
if you add up all the positive numbers, they equal less than nothing.
Veeky Forums btfo
Landon Evans
Isaiah Carter
Then why the hell does adding numbers eventually go to a lower number than where you start from discontinuously?
There's clearly one other system that behaves like this...
Jaxson Green
This is the quality of the content of the most popular mathematics youtube channel. Jesus christ
Easton Barnes
Someone help me understand why they take the average of natural numbers. If there's no meaningful value in the pattern between each N number, why would you take the average? That's where the fraction comes from, but it doesn't make any rigorous sense, and I say this as a mathematician.
Henry Phillips
It's called "analytic continuation". That's when a series doesn't converge, but analytic techniques are used to determine a specific numerical "result" for it anyway.
The classic example is the geometric series: the sum of x^n for all integers n > 0. If |x| < 1 then the series converges to 1/(1-x). If |x| >= 1 then the series diverges, but you can still often plug x into 1/(1-x) to get a result via analytic continuation.
Obviously, Σx^n is not the same function as 1/(1-x). Even though they yield exactly the same values for |x| < 1 -- that's not enough to conclude that they are the same function. You need agreement on the entire domain to claim that two functions are the same.
HOWEVER -- When one of the functions becomes undefined on some part of the domain, then you can use the other function to "extrapolate" (informally speaking) to get a "result" for the undefined function.
That's what people are doing when they claim that Σn has a "result" of -1/12. It doesn't really, but if you perform analytic continuation techniques on it (actually on a more general function called the "Riemann zeta function"), then you get -1/12 as a result of that analysis.
Hudson Gomez
m.youtube.com
Watch this entire video to understand what's going on.
Essentially, map the output of the riemann zeta function and notice its only defined for when the real part of s is greater than one.
The leap mathematicians do is say "well look at this graph, it makes an abrupt stop because we ran out of inputs. Let me reflect the graph vertically and now I have outputs for all complex numbers."
They literally just make up a mapping that LOOKS right because they just reflect the mapping function accross a vertical axis and say "there you go, everything is defined" and suddenly you get a lot of ridiculous formulas.
This is simply a useful mathematical tool, nothing more. Infinity doesn't equal -1/12 unless you suspend reality and make up shit.
Lucas Wilson
you can't actually add anything up to infinity unless you suspend reality so shut up
Jeremiah Allen
You can if each term is shrinking at a continuous rate. You shut up.
David Jackson
See here... the thing about this meme is that everyone should have said, "Oh! There is some problem with out analytical framework," but instead they said, "Fuck it! Let's go with it and point all the attention to the result but never the analytical framework!!!"
Asher Rivera
>the thing about this meme is that everyone should have said, "Oh! There is some problem with out analytical framework,"
I'm so tired of people with no grasp of what's going on saying shit like this. Everyone knows the series diverges and that the -1/12 value is an analytic continuation of a function that matches the series where its image is defined, not a "value of the series." It's just a fucking internet meme.