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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 4   Last Post: Sep 30, 2017 8:40 PM

 Messages: [ Previous | Next ]
 bursejan@gmail.com Posts: 5,511 Registered: 9/25/16
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Sep 30, 2017 8:35 PM

This doesn't mean that math or Newton cannot identify
some series as Cauchy, but if we had a black box:

+------+
| a_n |---> You
+------+

And you could take a ticket one by one with the
numbers of the sequence, you will never know whether

the series is Cauchy or not.

Am Sonntag, 1. Oktober 2017 02:32:08 UTC+2 schrieb burs...@gmail.com:
> 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
> >
> >
> > 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.?
> >
> > 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.

Date Subject Author
9/30/17 bursejan@gmail.com
9/30/17 bursejan@gmail.com
9/30/17 bursejan@gmail.com
9/30/17 bursejan@gmail.com