Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 15. Nov 2024, 11:04:33
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vh76bi$3bnde$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
On 14.11.2024 19:31, Jim Burns wrote:
On 11/14/2024 5:20 AM, WM wrote:
Here is a single claim which is true:
You don't say what reason you (WM) have
for knowing that that single claim is true.
It can be proven for every finite geometric figure that covering it by small pieces or intervals does not depend on the individuality and therefore on the order of the pieces.
That means if there is a configuration where the figure is not covered completely, every possible shuffling will also fail.
For infinite figures we use the analytical limit as is normal in mathematics.
Example:
XOOO...
XOOO...
XOOO...
XOOO...
...
One X per line is a density which can never be increased by reordering.
Regards, WM