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Topic: Proof 0.999... is not equal to one.
Replies: 194   Last Post: Feb 16, 2017 5:56 PM

 Messages: [ Previous | Next ]
 JEMebius Posts: 913 Registered: 12/13/04
Re: Proof 0.999... is not equal to one - is a joy for ever!
Posted: Sep 26, 2007 9:59 AM

mike3 wrote:
> On May 31, 12:16 am, chaja...@mail.com wrote:
>> I have written a proof that 0.999... cannot be equal to one in the
>> system of real numbers.
>>
>> While at the end of it all you may not fully agree with my proof, much
>> I as have never seen a proof asserting they were equal that I was able
>> to consider valid, I'm sure you will agree that the
>> ideas I present are not a simply rehashing of basic objections of
>> others before me.
>>
>>
>> --Charles J. Daniels
>> chaja...@mail.com

>
> _
> 0.9 must equal 1, however, at least in the real numbers. It may
> not in a system with infinitesimal/differential numbers but in
> _
> the reals 0.9 = 1, OK?
>

=======================================================================================

> I'd bet \$1,000,000 that your proof contains some sort of logical
> fallacy. Based on what bit of reading of it I did it seems like
> you are assuming a system where infinitesimals exist, but such
> a system is NOT the real numbers no matter how much you'd like it
> to be.

Proposal: The \$1,000,000.00 will be paid off not in a single installment, but rather as

\$900,000 + \$90,000 + \$9,000 + \$900 + \$90 + \$9 + \$0,90 + \$0,09 + \$0,09 +...,

often denoted as \$999,999.999,999,....., quite in the vein of this newsgroup.

Got the relation to a manner of long division in which one always leaves a non-zero
remainder (10 div 10 => quotient 0.9 remainder 1) so as to keep the ball rolling?

Johan E. Mebius

=======================================================================================

>
> "Again, the problem is introduced because decimal representation
> is not able to express or perceive a distance between a number
> that is infinite in position beyond the decimal point relative to
> other non-infinite decimals."
>
> Such a number is an infinitesimal, and thuse do not exist in the
> _
> reals. So 0.9, as a representation of a _real number_, *IS* equal
> to one.
>
> The other problem is that you seem to thin the definition of
> decimal system must be different. The sum
>
> sum_{n=-infinity...infinity} d_n B^n, 0 <= d_n < B
>
> is the _definition_ of the base-B repesentation of a real
> number!
> _
> For 0.9, d_n = 0 for n >= 0 and 9 for n < 0. The DEFINITION
> of infinite summation is
>
> sum_{n=-infinity...infinity} a_n =
> lim_{k->infinity} sum_{n=-k...k} a_n
>
> by DEFINITION, folks.
>
> This LIMIT equals ONE when a_n = 9 * 10^n when n < 0 and
> 0 when n >= 0. Since this Limit ***DEFINES*** the infinite
> sum and the infinite sum ***DEFINES*** the decimal then
> _
> 0.9 = 1, by DEFINITION.
>
> QED!!!
>
>
>

Date Subject Author
5/31/07 karl
5/31/07 karl
5/31/07 karl
5/31/07 Virgil
6/1/07 Richard Tobin
5/31/07 Glen Wheeler
5/31/07 The Ghost In The Machine
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
5/31/07 Glen Wheeler
5/31/07 Glen Wheeler
5/31/07 David W. Cantrell
6/5/07 Michael Press
5/31/07 Dr. David Kirkby
5/31/07 mensanator
5/31/07 mensanator
5/31/07 Jesse F. Hughes
5/31/07 Dik T. Winter
5/31/07 Rupert
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
2/2/17 JÃÂ¼rgen R.
2/2/17 abu.kuanysh05@gmail.com
5/31/07 William Hughes
5/31/07 Virgil
5/31/07 quasi
5/31/07 quasi
5/31/07 quasi
5/31/07 William Hughes
5/31/07 William Hughes
6/1/07 hagman
6/1/07 William Hughes
5/31/07 T.H. Ray
5/31/07 Jesse F. Hughes
5/31/07 T.H. Ray
5/31/07 Jesse F. Hughes
5/31/07 T.H. Ray
5/31/07 Jesse F. Hughes
5/31/07 Denis Feldmann
5/31/07 T.H. Ray
5/31/07 T.H. Ray
5/31/07 Dave Seaman
5/31/07 T.H. Ray
5/31/07 William Hughes
5/31/07 Jesse F. Hughes
6/1/07 Eric Schmidt
6/3/07 T.H. Ray
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
2/2/17 bassam king karzeddin
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
2/2/17 JÃÂ¼rgen R.
5/31/07 William Hughes
5/31/07 Dave Seaman
6/1/07 Glen Wheeler
5/31/07 William Hughes
6/1/07 William Hughes
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
5/31/07 Glen Wheeler
5/31/07 Marshall
6/5/07 Michael Press
5/31/07 bassam king karzeddin
5/31/07 Glen Wheeler
5/31/07 bassam king karzeddin
5/31/07 bassam king karzeddin
5/31/07 neilist
5/31/07 tommy1729
5/31/07 neilist
5/31/07 tommy1729
5/31/07 neilist
5/31/07 tommy1729
5/31/07 Dave Seaman
5/31/07 quasi
5/31/07 quasi
6/1/07 Dr. David Kirkby
6/1/07 quasi
6/1/07 hagman
5/31/07 hagman
6/1/07 Dr. David Kirkby
6/1/07 hagman
6/1/07 Eric Schmidt
6/1/07 hagman
6/2/07 hagman
5/31/07 Richard Tobin
5/31/07 mathedman@hotmail.com.CUT
5/31/07 Richard Tobin
5/31/07 William Hughes
5/31/07 Jesse F. Hughes
5/31/07 Brian Quincy Hutchings
5/31/07 Brian Quincy Hutchings
6/1/07 Richard Tobin
6/1/07 Jesse F. Hughes
6/1/07 Richard Tobin
6/1/07 Dik T. Winter
6/1/07 Jesse F. Hughes
6/1/07 Brian Quincy Hutchings
5/31/07 Dr. David Kirkby
5/31/07 quasi
5/31/07 quasi
5/31/07 quasi
6/1/07 Dr. David Kirkby
6/1/07 Virgil
6/1/07 Dr. David Kirkby
6/1/07 Dr. David Kirkby
6/1/07 Dik T. Winter
6/1/07 bassam king karzeddin
6/1/07 Dr. David Kirkby
3/22/13 John Gabriel
3/22/13 John Gabriel
6/1/07 Dr. David Kirkby
6/1/07 Denis Feldmann
2/7/13 Brian Q. Hutchings
2/8/13 JT
2/8/13 Virgil
2/8/13 JT
2/8/13 Virgil
2/8/13 Virgil
2/8/13 JT
2/8/13 Virgil
2/21/13 John Gabriel
6/1/07 JEMebius
6/1/07 bassam king karzeddin
2/2/17 bassam king karzeddin
6/1/07 mike3
9/26/07 JEMebius
9/26/07 mike3
9/27/07 Brian Quincy Hutchings
6/2/07 OwlHoot
6/3/07 jsavard@ecn.ab.ca
6/5/07 zuhair
6/10/07 Brian Quincy Hutchings
2/2/17 wolfgang.mueckenheim@hs-augsburg.de
2/2/17 JÃÂ¼rgen R.
2/2/17 Robin Chapman
2/2/17 JÃÂ¼rgen R.
2/2/17 R.J.Chapman
2/2/17 JÃÂ¼rgen R.
2/2/17 JÃÂ¼rgen R.
2/3/17 R.J.Chapman
2/8/17 George Cornelius
2/8/17 abu.kuanysh05@gmail.com
2/13/17 Dan Christensen
2/13/17 bassam king karzeddin
2/13/17 bursejan@gmail.com
2/15/17 William Hughes
2/15/17 netzweltler
2/15/17 William Hughes
2/15/17 William Hughes
2/15/17 netzweltler
2/15/17 William Hughes
2/15/17 netzweltler
2/15/17 Peter Percival
2/16/17 bassam king karzeddin
2/16/17 Peter Percival
2/15/17 William Hughes