Sujet : Re: Does the number of nines increase?
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 30. Jun 2024, 15:51:42
Autres entêtes
Organisation : Nemoweb
Message-ID : <kXNOUqhVO5RJr0ZVcChFHR1GHzc@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 30/06/2024 à 12:29, Jim Burns a écrit :
On 6/29/2024 2:14 PM, WM wrote:
If you think straight,
then only one conclusion follows:
0.999... < 1.
The values of infinite.length decimals
are assigned by a different method from how
the values of finite.length decimals are assigned.
0.999... ≠ 0.9 < 1
0.999... ≠ 0.99 < 1
0.999... ≠ 0.999 < 1
0.999... ≠ 0.9999 < 1
0.999... ≠ 0.99999 < 1
...
If you use only definable length, then always ℵo terms are missing.
All finite indices guarantee finite length. 0.999... = 0.999... < 1
0.999... = 1
That is wrong.
If you insert parentheses, nothing changes
..((((0,9)9)9)9)... = 0,999... 0.9 + 0.09 + 0.009 + ... contains ℵo terms with ℵo nines, all together smaller than 1.
Regards, WM
…