/sci/ - Science & Math

>>16138806

>>15977472

>>14886311
OP, let me explain it to you as someone who fell for the 1 + 2 + 3 + ... = -1/12 meme, i'm not a mathematician but i think i figured it out (an actual mathematician might correct me here)
This sum above is not convergent, anyone with a brain can see that, any "proof" you see with someone letting S = 1 + 2 + 3 + ... and then doing some tricks to show that S = -1/12 is an invalid proof because the order in which the terms are summed matters in an infinite series (you have to read how an infinite seires is defined to understand why)
When someone says 1 + 2 + 3 + ... = -1/12 then they are either dumb or they mean that when you define [eqn] Z:(1,\infty)\rightarrow \mathbb{R}^+ \\ Z(s) = \sum_{k=1}^\infty \frac{1}{n^s} [/eqn]Then take the analytic continuation of [math] Z [/math] and call it [math] \zeta [/math] then what we really mean by the above statement is that [math] \zeta(-1) = -1/12 [/math] which is not the same as saying [math] Z(-1) = -1/12 [/math] because these are not the same function but we often use the latter as a shorthand for the former.

>>14886443
>How many apples would that be?
"1 Real projective plane embedding into [math]\mathbb{R}^3[/math]" Apples

>>14885263