Date: Sep 30, 2017 8:23 PM
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 say
he used limits. But how do you get limits, without

knowing whether a series converges or not? For convergence
you need to make statement about infinitely many elements,

for example the Cauchy condition, is for infinitely many
pairs n,m, namely you need to know (or assume you know):

forall n,m >= N(e) |an - am| =< e

The above looks like a pi-sentence, and is not verifiable
if 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.?

Am 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
> > >>
> > >> .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.