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Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted:
Sep 30, 2017 8:23 PM


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.



