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Topic:
What is a series? Reeducating mainstream orangutans is like trying to convert ISIS to Christianity.
Replies:
1
Last Post:
Oct 6, 2017 3:10 PM




Re: What is a series? Reeducating mainstream orangutans is like trying to convert ISIS to Christianity.
Posted:
Oct 6, 2017 3:10 PM


Den fredag 6 oktober 2017 kl. 20:15:21 UTC+2 skrev John Gabriel: > What is a series? Reeducating mainstream orangutans is like trying to convert ISIS to Christianity. > > In a previous thread I explained how Newton arrived at his ideas about series. Of course the orangutans of mainstream screamed loud and hard because that's what orangutans do. > > A series is CHARACTERISED by its GENERAL TERM or nTH PARTIAL SUM. > > EVERYTHING we know about ANY series in terms of LIMITS, is determined from its nTH PARTIAL SUM. > > There is NO difference between > > 0.3+0.03+0.003 [A] > > and > > 0.3+0.03+0.003+... [B] > > except for the ellipsis which tells us that the object we are dealing with is not a standard number, but a series with no last term. > > [A] is a number. All numbers are FINITE series. > > [B] is a FINITE series with the attribute that it has no last term and is thus INDETERMINABLE. > > There is no such thing as an INFINITE series which does not exist outside your dysfunctional minds. > > Potential and actual infinity are Cantorian nonsense. > > 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. > > gilstrang@gmail.com (MIT) > huizenga@psu.edu (HARVARD) > andersk@mit.edu (MIT) > david.ullrich@math.okstate.edu (David Ullrich) > djoyce@clarku.edu > markcc@gmail.com
This is wrong. A series is a limit of its partial sums. A series is not literary an addition of infinitely many terms. That's a plain stupid and nonsensical strawman. There IS a difference between 0.3+0.03+0.003 and 0.3+0.03+0.003+...
0.3+0.03+0.003 is a finite sum and the rational number 0.333 = 333/1000. 0.3+0.03+0.003+... is a limit and equal to the rational number 1/3.
Series = infinite sum = limit of finite sum
This isn't too hard to understand.



