Re: Does the number of nines increase?

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