Date: Oct 6, 2017 11:01 AM
Author: bursejan@gmail.com
Subject: Re: reason why 1=.99999....99(10/9) and why 1/3 = .333333......33(1/3),<br> never that nonsense 1=.999.... 1/3 = .3333.....

Dont ask so difficult questions, AP brain farto
cannot answer. He is even not aware that Newton

introduced compleat Quotients to calculate with
rational numbers, and that for example sqrt(2)

doesn't have compleat Quotient representation.
Newton doesn't use our modern name rational

numbers, but he writes:
"This method of reduction (*) may be thus very
conveniently imitated in numbers..."
https://archive.org/stream/methodoffluxions00newt#page/162/mode/2up

An it appears in book part called "Annotations",
so I guess its not from Newton himself.

sqrt(2) comes only later, and for example on page
171 the author atributes some of the developments

to A. D. Moivre:

In the theory of series, de Moivre developed a
polynomial theorem encompassing Newton's binomial
theorem and, in particular, a theorem of recurrent
series useful in the calculus of probability.
https://link.springer.com/article/10.1007/BF00411630

(Thats maybe also where Euler got his diverging
series from, not sure)

(*)
The geometric series from the previous section.


Am Freitag, 6. Oktober 2017 16:48:01 UTC+2 schrieb Markus Klyver:
> Den tisdag 3 oktober 2017 kl. 04:21:37 UTC+2 skrev Archimedes Plutonium:
> > Newsgroups: sci.math
> > Date: Mon, 2 Oct 2017 08:32:50 -0700 (PDT)
> >
> > Subject: Why is there a difference between fractions 1/3 and .333 repeating
> > multiplied by 3
> > From: Archimedes Plutonium <plutonium....@gmail.com>
> > Injection-Date: Mon, 02 Oct 2017 15:32:50 +0000
> >
> >
> > Because you cannot mix fraction with a decimal unless the decimal ends in 0's
> >
> > For example 10 divided by 3 is 10/3 or written as 3+1/3
> >
> > But completely wrong when writing it as 3.333.... Because the dots mean nothing, unless you write it as 3.3333...33(1/3) so you include the carryover at infinity
> >
> > This means that .99999.... is not 1, unless you included the carryover at infinity border as this
> >
> > .99999....99(10/9) which in fact is 1
> >
> > For you divide 10 by 9 carry the 1 leaving behind 0, 1 added to 9 is 10, carryover the 1, leaving behind another 0, finishing off with
> >
> > .9999....99(10/9) = 1.0000.....
> >
> > You see Old Math was too dumb and lazy to define how those dots ......... Interfaces with fractions, too dumb too lazy
> >
> > AP
> >
> > Newsgroups: sci.math
> > Date: Mon, 2 Oct 2017 19:10:39 -0700 (PDT)
> >
> > Subject: the reason why 1=.99999....99(10/9) and why 1/3 = .333333......33(1/3)
> > From: Archimedes Plutonium <plutonium....@gmail.com>
> > Injection-Date: Tue, 03 Oct 2017 02:10:39 +0000
> >
> > the reason why 1=.99999....99(10/9) and why 1/3 = .333333......33(1/3)
> >
> > On Monday, October 2, 2017 at 10:33:05 AM UTC-5, Archimedes Plutonium wrote:

> > > Because you cannot mix fraction with a decimal unless the decimal ends in 0's
> > >
> > > For example 10 divided by 3 is 10/3 or written as 3+1/3
> > >
> > > But completely wrong when writing it as 3.333.... Because the dots mean nothing, unless you write it as 3.3333...33(1/3) so you include the carryover at infinity
> > >
> > > This means that .99999.... is not 1, unless you included the carryover at infinity border as this
> > >
> > > .99999....99(10/9) which in fact is 1
> > >
> > > For you divide 10 by 9 carry the 1 leaving behind 0, 1 added to 9 is 10, carryover the 1, leaving behind another 0, finishing off with
> > >
> > > .9999....99(10/9) = 1.0000.....
> > >
> > > You see Old Math was too dumb and lazy to define how those dots ......... Interfaces with fractions, too dumb too lazy
> > >
> > >

> >
> > Alright, let me expand and expound on the ideas above, of undefined and ignorant dots .............
> >
> > The snobs, and slobs of Old Math who think that 1/3 = .333333..... and that 1 = .999999.....
> >
> > Well, ask those slobs and snobs, ask them to add
> >
> > 0.9999999.....
> > +.9999999.......
> >
> > watch the goon squad try to get rid of this 1.99999.....9998
> >
> > ask the goon squad how they got rid of the "8"
> >
> > But, on the other hand, when you well define the ellipsis, for those series of dots ...... is called Ellipsis
> >
> > If you well define the ellipsis with an infinity border and where you include all REMAINDERS in division.
> > Then you have a correct and proper mathematics.
> >
> > The example that must always be followed in division is the remainder
> >    ________
> > 3| 1000       = 333+1/3
> >
> > We never imagine that the correct final answer is without that fraction 1/3 added on
> >
> > Thus, when we have
> >
> >    ________
> > 3| 1.000...       = .333....(+1/3)
> >
> > for we have a ending fraction of (+1/3)
> >
> > Now, the slobs and snobs never realized how important that (+1/3) was for they boneheadedly did this
> >
> > .3333333333.......... plus .3333333...........  = .666666666........ and thought everything was A-okay
> >
> > But look what the true addition is like:
> >
> > .333333.....33(+1/3) + .333333.....33(+1/3) = .66666666........66(+2/3)
> >
> > You see how unmessy that is, because, well look at this by the boneheads:
> >
> > .99999999..... + .99999999..... = 1.999999......998
> >
> > Whereas true math has
> >
> > .9999999......99(+10/9) + .9999999.....99(+10/9) = 1.999999.....98(+20/9) = 2.00000....(+0)
> >
> > So, you see how clean that all is, rather than what the slobs, snobs and boneheads dish out in their fantasies of math.
> >
> > They are failures, regular failures of math for they refuse to define infinity with a borderline and then they make up this crap that .9999.... is the same as 1, or that .33333.... is the same as 1/3 when they forgot about the remainder.
> >
> > AP

>
> 1) Do you understand that decimal expansions are defined in terms of limits?
>
> 2) Do you understand limits?