JT
Posts:
436
Registered:
4/7/12
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Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 14, 2013 12:15 PM
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On 13 mar, 20:07, fom <fomJ...@nyms.net> wrote:
> On 3/13/2013 9:57 AM, JT wrote:
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> > On 13 mar, 15:48, JT <jonas.thornv...@gmail.com> wrote:
> >> On 13 mar, 15:39, JT <jonas.thornv...@gmail.com> wrote:
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> >>> On 13 mar, 14:42, JT <jonas.thornv...@gmail.com> wrote:
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> >>>> On 13 mar, 13:58, JT <jonas.thornv...@gmail.com> wrote:
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> >>>>> On 13 mar, 10:42, fom <fomJ...@nyms.net> wrote:
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> >>>>>> On 3/12/2013 10:24 PM, Virgil wrote:
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> >>>>>>> In article <f93df84b-f04d-434c-832e-d458c0df9b2c@googlegroups.com>,
> >>>>>>> spermato...@yahoo.com wrote:
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> >>>>>>>> On Wednesday, March 13, 2013 11:19:51 AM UTC+11, 1treePetrifiedForestLane
> >>>>>>>> wrote:
> >>>>>>>>> yes, and the proper infinite series with which
>
> >>>>>>>>> it is to be compared, is the "real number,"
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> >>>>>>>>> 1.0000..., not omitting any of the zeroes
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> >>>>>>>>> on your little blackboard, dood.
>
> >>>>>>>>> see Simon Stevins; *creation* of teh decimals,
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> >>>>>>>>> including this sole ambiguity, 15cce.
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> >>>>>>>>>> It s a symbol which represents an "infinite series",
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> >>>>>>>>>> which in turn is a sequence.
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> >>>>>>>> yesw but .9999... is a non-finite number
> >>>>>>>> and 1.0000.. is a finite number
> >>>>>>>> thus
> >>>>>>>> when maths shows
> >>>>>>>> .9999... is a non-finite number = 1.0000.. is a finite number
> >>>>>>>> it ends in contradiction
>
> >>>>>>> 0.9999... and 1.0000... are numerals (names of numbers), not numbers.
> >>>>>>> They are only different names for the same number.
>
> >>>>>> And, in addition, to say that 1.000... is
> >>>>>> finite may also be arguable.
>
> >>>>>> As names, decimal expansions are what they
> >>>>>> are. 1.000... expresses a particular name
> >>>>>> exactly. Without the full expression, one
> >>>>>> must consider scenarios involving rounding
> >>>>>> error. In that case, the finite representation
> >>>>>> corresponds to an equivalence class of
> >>>>>> decimal expansions that round to whatever
> >>>>>> finite number of significant digits specifies
> >>>>>> the system of finite abbreviation.
>
> >>>>>> To say that 1.000... is finite without
> >>>>>> qualification is to invoke a convention that
> >>>>>> is not intrinsic to the system of names that
> >>>>>> grounds the representation.
>
> >>>>>> Of course, it is a common convention...
>
> >>>>>> ...that ought not invalidate mathematics.
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> >>>>> Silly man 0 is not a mathematical object it have no magnitude when
> >>>>> used for counting and measuring it is just a label that an operation
> >>>>> exhausted it's operands.
>
> >>>> 0.999... is just a label unfortunatly the context it try to label 1
> >>>> within is incorrect to start with something with unfinished decimal
> >>>> expansion is just an approximation, change base.
> >>>> 0.3 in ternary is a correct label in fact it *is* 1 thus you are free
> >>>> to write 0.3 or 1 in ternarys, this is not true for decimal
> >>>> numbersystem 0.999... do not equal 1, because you can not create the
> >>>> set that makes up 1 adding the members of the set ->
> >>>> {0.9,0.09,0.009 ...}!= 1 there is no set at this form that equals 1,
> >>>> but in ternarys we have no problem to write that the sum of members in
> >>>> the set {0.1,0.1,0.1} = 1
>
> >>> And of course the sum of members in the set
> >>> {0.333...,0.333...,0,333...}!=1 since 1/3 can not be expressed in
> >>> decimal change base use ternary or use fractions. The label 0.333...
> >>> express a number that is not available in decimal base, since it is
> >>> impossible to partition a single natural entity in such away that 1/3
> >>> is reached.
>
> >> Plato did understand the difference between naturals and the parts
> >> that make them up alot better then modern mathematicians, thus he
> >> understood the principles of partitioning and thus recognized that
> >> fractions was the only way to deal with decimal expansion with out
> >> losing digits since there is no base system that can express all
> >> possible fractions.
>
> > And the truth that Plato understood but that modern mathematicians
> > clueless about is that naturals is a countable bottom up approach thus
> > they must be discrete in nature, and following this that each natural
> > have a magnitude that could be partitioned, but he also understood the
> > drawbacks of using a base for partition because he realised that in a
> > continum there is an endless amount cuts can be made and there is no
> > single base number system that can express them all, and from that he
> > draw the conclusion that fractions was the only way to deal with parts
> > of a single discrete natural entity.
>
> You really just go on and on...
>
> Like the energizer bunny.
>
> Aristotle disagreed with Plato long before Western mathematics
> considered the possibility of 0. Since Aristotle, at least,
> mathematicians have had to make choices as to whose authority
> they would follow if they chose not to follow their own ideas.
>
> Even then, the very words you use in your criticisms probably
> originate from the work of Vieta (one must have polynomials
> before one recognizes the general form of a base). It is with
> Vieta that geometric magnitudes and monadic units are treated
> uniformly as numbers.
>
> You need to make your criticisms without using the mathematics
> with which you disagree.
So you have no critisism on NyaN bases, can you see why 1 equals 0.3
in ternary using a zeroless NyaN base. Could you see any computational
gains, drawbacks using NyaN base in arithmetic circuits instead of
standard numerical bases. I disagree with any numbersystem
incorporating 0 as an evaluable numerical entity in an evaluation, it
is as simple as that, zero maybe a useful term/label for exhausted
operands mathematical expression interpretated by man but for an
arithmetic circuit it is a waist of time (cycles).
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