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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




Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted:
Sep 30, 2017 8:40 PM


Math can even reason, that if these two boxes are Cauchy, i.e. the series {an} and {bn}: ++  a_n > You ++
++  b_n > You ++
That then the following series will be Cauchy as well, namely the product series {an*bn}:
++  a_n*b_n > You ++
You can construct the product series, this is observable, you can just combine the two black boxes and create a new black box. If each black box,
gives a rationl number, you can build a new black box, for the product, but still being Cauchy is not effectively refutable or effectively verifiable.
We only proved a formal implication:
{an}, {bn} Cauchy ==> {an*bn} Cauchy
That {an*bn} is observable is rather trivial, and that Newton could also do it is to expect. But if you can construct {an*bn} doesn't mean you have solved the limit problem for unknown series.
Am Sonntag, 1. Oktober 2017 02:35:38 UTC+2 schrieb burs...@gmail.com: > 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: > > > > anam > 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 anam=<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 > > > > > > The above looks like a pisentence, 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 UTC5, 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 illformed definition  the Eulerian Blunder.



