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

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 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,394 Registered: 10/18/08
Re: Proof 0.999... is not equal to one.
Posted: Feb 2, 2017 8:26 AM
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Am Donnerstag, 31. Mai 2007 16:07:56 UTC+2 schrieb William Hughes:
> On May 31, 8:01 am, chaja...@mail.com wrote:
> > > You do however have to give some sort of definition for 0.999...
> > > Whatever you define it to be it will either be equal to 1
> > > or it will not be a real number.

> >
> > My definition of 0.999... is the sum of all elements of an infinite
> > set defined by 0.9*(1/10)^n for all n in the set of wholes numbers
> > including 0 and is included in my proof.

>
> You are defining 0.999... in terms of something else
> you have not defined, the sum of all elements of an infinite
> set. The standard definition uses a limit and produces
> a real number.

The "standard definition" however is overridden by set theory. There we have as a limit the complete sequence of all indexed nines. We have a bijection between omega and the set of all indexed nines. Note that omega is not among the natural numbers. According to this fact 1 is not among all terms of the sequence.

REgards, WM

Date Subject Author
5/31/07 chajadan@mail.com
5/31/07 karl
5/31/07 chajadan@mail.com
5/31/07 karl
5/31/07 chajadan@mail.com
5/31/07 karl
5/31/07 chajadan@mail.com
5/31/07 Virgil
6/1/07 chajadan@mail.com
6/1/07 Richard Tobin
5/31/07 pomerado@hotmail.com
5/31/07 chajadan@mail.com
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 chajadan@mail.com
5/31/07 chajadan@mail.com
5/31/07 Glen Wheeler
5/31/07 chajadan@mail.com
5/31/07 David W. Cantrell
5/31/07 chajadan@mail.com
6/5/07 Michael Press
5/31/07 Dr. David Kirkby
5/31/07 mensanator
5/31/07 chajadan@mail.com
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 chajadan@mail.com
5/31/07 chajadan@mail.com
5/31/07 Virgil
5/31/07 chajadan@mail.com
5/31/07 quasi
5/31/07 chajadan@mail.com
5/31/07 quasi
5/31/07 chajadan@mail.com
5/31/07 quasi
5/31/07 William Hughes
5/31/07 chajadan@mail.com
5/31/07 William Hughes
6/1/07 hagman
6/1/07 chajadan@mail.com
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 chajadan@mail.com
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
5/31/07 chajadan@mail.com
6/1/07 Eric Schmidt
6/1/07 chajadan@mail.com
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 chajadan@mail.com
5/31/07 Dave Seaman
5/31/07 chajadan@mail.com
6/1/07 Glen Wheeler
5/31/07 William Hughes
6/1/07 chajadan@mail.com
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 chajadan@mail.com
5/31/07 Dave Seaman
5/31/07 quasi
5/31/07 chajadan@mail.com
5/31/07 quasi
6/1/07 Dr. David Kirkby
6/1/07 quasi
6/1/07 chajadan@mail.com
6/1/07 hagman
6/1/07 chajadan@mail.com
5/31/07 hagman
5/31/07 chajadan@mail.com
6/1/07 Dr. David Kirkby
6/1/07 hagman
6/1/07 chajadan@mail.com
6/1/07 Eric Schmidt
6/1/07 chajadan@mail.com
6/1/07 hagman
6/1/07 chajadan@mail.com
6/2/07 hagman
6/18/07 chajadan@mail.com
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 chajadan@mail.com
6/1/07 Richard Tobin
6/1/07 chajadan@mail.com
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 chajadan@mail.com
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 chajadan@mail.com
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 chajadan@mail.com
6/1/07 Denis Feldmann
6/1/07 chajadan@mail.com
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

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