Moments in history that saved /sci/
That was so astounding that people called it fake
>the sum of all positive integers is -1/12>What do you mean math is broken? No this is the right answer!
>>16820003Reminder that Ramanujan dilated and was in a mistresscoded relation with Hardy.
>>16820015SAAR DO NOT REDEEM THE SUMDO NOT REDEEM
>>16820015Why not? If you can define "sum" to mean "the limit of a convergent sequence of partial sums" and claim you thereby did an infinite number of plus operations, you can also define "sum" to mean whatever Ramanujan dreamed up.
>>16820048This. The people seething over the video don't even understand the definition of an infinite sum.
>the sum of all positive integers equalling -1/12 does make sense because... because it just does OKAY! You just don't get it.
>>16820003so does that mean any lim 1/n =/= 0?
>>16820003don't forget the follow uphttps://www.youtube.com/watch?v=beakj767uG4
>>16820831depends on what you mean by sum, yes
I hate this stupid garbage. One look at pic rel tells you everything you need to know about this retarded bullshit.
>Coverage of this topic in Smithsonian magazine describes the Numberphile video as misleading and notes that the interpretation of the sum as −+1/12 relies on a specialized meaning for the equals sign, from the techniques of analytic continuation, in which equals means is associated with.[35] The Numberphile video was critiqued on similar grounds by German mathematician Burkard Polster on his Mathologer YouTube channel in 2018, his video receiving 2.7 million views by 2023.[36]Imagine getting btfo this hard
>>16820770[eqn]S = 2^0+2^1+2^2+...\\2S = 2(2^0+2^1+2^2+...)\\2S = 2^1+2^2+2^3+...\\S-1 = 2^0+2^1+2^2+... -1\\S-1 = 1+2^1+2^2+... -1\\S-1 = 2^1+2^2+...\\2S = S-1\\S = -1\\[/eqn]
>>16820770Crying about this is tantamount to crying about x^2+1=0 having solutions. It's a matter of definitions and conventions, if it leads to useful and consistent maths then there is no reason not to use it as long as you properly describe the concept, which numberphile didn't.
>>16821547>>16821552>>16821541
I miss when this boad was all about /sci/entists talking about classes or sharing their weird ass projects instead of /pol/ and /x/ fags spamming schizo bullshit and tiktok scams.
>>16821586interesting part about this is that 2S and S-1 are not exactly equal if you take into account the positions of each partial sum.
