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


Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 13, 2013 10:52 AM


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 he knew that the natural numbers did not include zero and that they were discrete in nature thus naturals without zero, he also knew that each natural had a continuum of infinitsmalls that defied partitioning since they were countless in terms of numbers, thus he wisely chosed to go for fractions.
Whatever modern mathematicians like to think Plato mathematical skills were way behind their reach.

