```Date: Sep 30, 2017 8:23 PM
Author: bursejan@gmail.com
Subject: Re: It is a very bad idea and nothing less than stupid to define 1/3<br> = 0.333...

Well you wrote here Newton didn't consider infinity,and you say he can define partial sums without infinity.Well this might be true, but you then go on and sayhe used limits. But how do you get limits, withouthttps://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJknowing whether a series converges or not? For convergenceyou need to make statement about infinitely many elements,for example the Cauchy condition, is for infinitely manypairs n,m, namely you need to know (or assume you know):   forall n,m >= N(e) |an - am| =< eThe above looks like a pi-sentence, and is not verifiableif we do not know much about {ak}. So you are in the waters of:It is also familiar in the philosophy of science that most hypotheses are neither verifiable nor refutable. Thus, Kant?s antinomies of pure reason include such statements as that space is infinite, matter is infinitely divisible, and the series of efficient causes is infinite. These hypotheses all have the form  forall x exists y P(x, y).For example, infinite divisibility amounts to ?for every product of fission, there is a time by which attempts to cut it succeed? and the infinity of space amounts to ?for each distance you travel, you can travel farther.?https://www.andrew.cmu.edu/user/kk3n/complearn/chapter11.pdfAm Sonntag, 1. Oktober 2017 00:58:40 UTC+2 schrieb John Gabriel:> On Saturday, 30 September 2017 17:25:16 UTC-5, FromTheRafters  wrote:> > netzweltler explained on 9/30/2017 :> > > Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:> > >> > > >> .9 repeating and One share a sameness. They are quantities> > >> that are different by the infinitely small.> > >> .9 repeating is a transcendental One; the First quantity> > >> below one. The infinitely small difference means a shared> > >> sameness that is still not absolutely same.> > >> > > >> Mitchell Raemsch> > >> > > If there is a quantity between 0.999... and 1 and, therefore, these are two > > > different points on the number line then you should define the distance > > > between these two points. If you don't, then your first quantity is simply > > > undefined. > > >> > > 'infinitely small' is not a definition. There are no two distinct points on > > > the number line 'infinite(simal)ly' far away from each other.> > > > They do not differ> >    by infinite small.> > They differ only> >    by none at all.> > Well, if you define 0.999... to be equal to a brick, then a brick and 0.999... differ by none at all.> > There is not a single support for this bullshit equality aside from S = Lim S and this is an ill-formed definition - the Eulerian Blunder.
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