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.