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Topic: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017

Replies: 40   Last Post: Jan 4, 2018 7:37 AM

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wolfgang.mueckenheim@hs-augsburg.de

Posts: 3,394
Registered: 10/18/08
Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017

Posted: Dec 28, 2017 4:49 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Am Donnerstag, 28. Dezember 2017 21:09:48 UTC+1 schrieb konyberg:
> torsdag 28. desember 2017 08.28.04 UTC+1 skrev WM følgende:


> > > This is not a proof as such, but it's a reasonable construction.
> > > 1 = 9/9 = 1/9 + 8/9 = 0.111... + 0.888... = 0.999...
> > > Show me what's wrong with this.

> >
> > This is wrong: 1/9 + 8/9 = 0.111... + 0.888...
> >
> > Correct would be 1/9 + 8/9 = lim{n-->oo} 0.111...1_n + lim{n-->oo} 0.888...8_n


>
> Does it change the result?


Yes, in case of irrationals. A sum of fractions will not yield an irrational value. The belief that infinitely many fractions could yield an irrational is a silly as the belief that infinitely many red points would yield a green line.

A digit sequence does not define its limit. That can only be done by finite formula defining this digit sequence. A Cantor-diagonal is never a transcendental and cannot define it.

One of the wrong "results" is the idea that Cantor proved the existence of transcendental numbers and the idea that the measure of the reals is 1 and the measure of the rationals is 0 in the unit interval.

Regards, WM



Date Subject Author
12/27/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Karl-Olav Nyberg
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bursejan@gmail.com
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bursejan@gmail.com
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Jan Burse
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Python
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Karl-Olav Nyberg
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Python
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bursejan@gmail.com
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bursejan@gmail.com
12/29/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/29/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/28/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/29/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/30/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/30/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
7777777
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
7777777
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
1/4/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bassam king karzeddin
12/30/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/30/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
LudovicoVan
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find p/q such that 0.999... = p/q. 12/26/2017
FromTheRafters
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
1/2/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
1/2/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
1/2/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
1/3/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
1/4/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
zelos.malum@gmail.com
1/4/18
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
wolfgang.mueckenheim@hs-augsburg.de
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
bassam king karzeddin
12/31/17
Read Re: If you claim 0.999... is a rational number, then you must find
p/q such that 0.999... = p/q. 12/26/2017
Dan Christensen

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