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