JT
Posts:
436
Registered:
4/7/12
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Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 13, 2013 10:39 AM
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On 13 mar, 14:42, JT <jonas.thornv...@gmail.com> wrote:
> 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
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> > > >>> 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.
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> > > >>> 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
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> > > > 0.9999... and 1.0000... are numerals (names of numbers), not numbers.
> > > > They are only different names for the same number.
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> > > And, in addition, to say that 1.000... is
> > > finite may also be arguable.
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> > > 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.
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> > > 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.
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> > > Of course, it is a common convention...
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> > > ...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.
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> 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.
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