Date: Oct 6, 2017 3:10 PM
Author: Markus Klyver
Subject: Re: What is a series? Reeducating mainstream orangutans is like<br> trying to convert ISIS to Christianity.

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.