onsdag 27. september 2017 18.05.46 UTC+2 skrev konyberg følgende: > onsdag 27. september 2017 14.20.13 UTC+2 skrev John Gabriel følgende: > > On Monday, 25 September 2017 19:22:51 UTC-4, John Gabriel wrote: > > > https://www.linkedin.com/pulse/part-1-axioms-postulates-mathematics-john-gabriel > > > > > > https://www.linkedin.com/pulse/part-2-axioms-postulates-mathematics-john-gabriel > > > > > > https://www.linkedin.com/pulse/part-3-axioms-postulates-mathematics-john-gabriel > > > > > > https://www.linkedin.com/pulse/part-4-axioms-postulates-mathematics-john-gabriel > > > > > > https://www.linkedin.com/pulse/part-5-axioms-postulates-mathematics-john-gabriel > > > > > > Comments are unwelcome and will be ignored. > > > > > > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics. > > > > > > email@example.com (MIT) > > > firstname.lastname@example.org (HARVARD) > > > email@example.com (MIT) > > > firstname.lastname@example.org (David Ullrich) > > > email@example.com > > > firstname.lastname@example.org > > > > Here is a quote from the only mainstream academic I respect on sci.math: > > > > > > Euler's teacher was Johann Bernoulli, the more conceited and less genial of the Bernoulli brothers (of course being "less genial" than Jakob B does not mean a reproach). Euler was even more genial than both and many others. Nevetheless here he applied the wrong concept. > > > > John Gabriel is completely correct when he says: > > > > 1. S = Lim S, is wrong > Of course it is wrong! Euler never wrote that! > > 2. The series is not the limit. > Of course not if a series is defined as finite. But if the series is defined as the infinite sum, then it is the limit. > > 3. 1/3 cannot be expressed in base 10 because 3 is not a prime factor of 10. > This, and both 1. and 2. is your own invention. Who is the good professor It is WM! > > KON > > > > Unfortunately the contrary belief has lead to the mess of transfinite set theory. > > > > Regards, WM
Ok. Some questions for you, JG. S(n) = (i=0 to n)Sum ((-1)^i a^i)), |a| < 1 What is this? Can you give me the closed form?
And where do this lead to? S = (n=0 to inf)Sum ((-1)^n a^n)), |a| <1 Can you give me the closed form of this?
Is it the same as the former?
Is it: S(n) = S, or lim S(n) = S, or S(n) = lim S(n), or S = lim S. What do you go for, and what would Euler go for?