JT
Posts:
1,150
Registered:
4/7/12


Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 13, 2013 10:39 AM


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.

