Den söndag 1 oktober 2017 kl. 15:17:49 UTC+2 skrev John Gabriel:
> On Saturday, 30 September 2017 19:32:08 UTC-5,
burs...@gmail.com wrote:
> > So the product, its terms sn*tn might be observable,
> > but that the product is Cauchy is not observable directly.
> >
> > That a series is Cauchy is neither effectively refutable
> > nor effectively verifiable. If you find e, n, m with:
> >
> > |an-am| > e
> >
> > You still don't know whether there is N, where the series
> > behaves Cauchy. The full Cauchy condition is:
> >
> > forall e exists N forall n,m>=N |an-am|=<e
> >
> > So it has the shape VEV.
> >
> > Am Sonntag, 1. Oktober 2017 02:23:32 UTC+2 schrieb
burs...@gmail.com:
> > > 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
> > >
> > >
https://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJ
> > >
> > > 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
>
> Each time I think you can't say anything more stupid, you surprise me.
> Listen stupid, the forall you have there is based on induction. There is no forall. A Cauchy sequence does not require "forall". The "forall" is a result of inference.
>
> > >
> > > 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.”
> > >
> > >
https://www.andrew.cmu.edu/user/kk3n/complearn/chapter11.pdf
> > >
> > > 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
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.
Sure is, for all statement made by John Gabriel, none of them is correct.