söndag 10 november 2019 kl. 16:32:33 UTC+1 skrev Eram semper recta:
> Rudin's Bullshit book is referenced:
>
> https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_mathematical_analysis_walter_rudin.pdf
>
>
> On Page 59 (Page 68 of PDF) we have:
>
> ---------
> s = \sum_{n=1}^{\infty} a_n
>
> The number s is called the sum of the series; but it should be clearly understood that s is the limit of a sequence of sums, and is not obtained simply by addition.
>
> ---------
>
> Notice that is states clearly:
>
> BUT it should be clearly understood that s is the LIMIT of a SEQUENCE of SUMS, and is NOT obtained simply by ADDITION.
>
> So, a series is simply a partial sum. There is NO such thing as an infinite series. 0.3+0.03+0.003+... is NOT an infinite series but a partial sum 0..3+0.03+0.003 followed by "+...". Nothing more, nothing less. It is 100% FINITE. Get it morons?
>
> Next, a sequence is obtained from a series. Any guesses? Chuckle.
>
> Right! The terms of a sequence are obtained from the partial sums of a series. In the example 0.3+0.03+0.003, the partial sums are given by:
>
> {S(1); S(2); S(3); ...}
>
> where
>
> S(n) = (1/3)*[1-10^(-n)]
>
> Okay so far you incorrigibly stupid cunts?
>
> Now, in analysis, we consider what happens as the number of terms in any partial sum increases indefinitely. NOTHING about "infinity" there you syphilitic bastards!!!!!
>
> S(n) = 1/3 - 1/(3*(10^n))
>
> IF n increases indefinitely, THEN 1/(3*(10^n)) decreases indefinitely. No imbeciles, 1/(3*(10^n)) NEVER becomes ZERO. Now, IF 1/(3*(10^n)) increases indefinitely, THEN the partial sum 1/3 - 1/(3*(10^n)) increases indefinitely to 1/3, but NEVER becomes 1/3.
>
> All this elementary crap was taught in high school. Unfortunately, the morons who followed Euler's S = Lim S, imagined that s = S(oo). In other words, the fools imagined that an infinite sum is possible. Sound weird?! Of course!!!!
>
> Don't fall for this bullshit but call out the moron who tries to peddle this in your class lest you become a prize idiot like one of your mainstream mythmatics professors.
>
> YOU HAVE BEEN WARNED.
But that is not what the text says. The text says that s is the limit of a sequence of the partial sums. A series is not a partial sum. It is the limit.