JT
Posts:
1,448
Registered:
4/7/12


Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 14, 2013 12:15 PM


On 13 mar, 20:07, fom <fomJ...@nyms.net> wrote: > On 3/13/2013 9:57 AM, JT wrote: > > > > > > > > > > > On 13 mar, 15:48, JT <jonas.thornv...@gmail.com> wrote: > >> On 13 mar, 15:39, JT <jonas.thornv...@gmail.com> wrote: > > >>> On 13 mar, 14:42, JT <jonas.thornv...@gmail.com> wrote: > > >>>> On 13 mar, 13:58, JT <jonas.thornv...@gmail.com> wrote: > > >>>>> On 13 mar, 10:42, fom <fomJ...@nyms.net> wrote: > > >>>>>> On 3/12/2013 10:24 PM, Virgil wrote: > > >>>>>>> In article <f93df84bf04d434c832ed458c0df9b2c@googlegroups.com>, > >>>>>>> spermato...@yahoo.com wrote: > > >>>>>>>> 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," > > >>>>>>>>> 1.0000..., not omitting any of the zeroes > > >>>>>>>>> on your little blackboard, dood. > > >>>>>>>>> see Simon Stevins; *creation* of teh decimals, > > >>>>>>>>> including this sole ambiguity, 15cce. > > >>>>>>>>>> It s a symbol which represents an "infinite series", > > >>>>>>>>>> which in turn is a sequence. > > >>>>>>>> yesw but .9999... is a nonfinite number > >>>>>>>> and 1.0000.. is a finite number > >>>>>>>> thus > >>>>>>>> when maths shows > >>>>>>>> .9999... is a nonfinite 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. > > >>>>> 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).

