Talk:Cantor's diagonal argument/Arguments: Difference between revisions

Content deleted Content added
Tag: Reverted
Undid revision 1283956705 by Trovatore (talk) I suppose you can argue that infinitely many leading zeroes don't matter. Anyway the point isn't worth discussing
Line 1,346:
 
:They don't become the natural numbers. Almost all of them will be infinitely long, and there are no infinitely long natural numbers. [[User:MartinPoulter|MartinPoulter]] ([[User talk:MartinPoulter|talk]]) 08:48, 3 April 2025 (UTC)
:::<small>Actually all of them will be infinitely long. Not that it matters. There aren't any "terminating decimals", just ones that end in 000.... --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 18:23, 4 April 2025 (UTC) </small>
::That is only true if you don't allow natural numbers to be [[Actual infinity|actual infinite]], which does not make any sense in an infinite universe. [[Special:Contributions/2A02:8109:40B:EF00:F805:A5D1:158:660B|2A02:8109:40B:EF00:F805:A5D1:158:660B]] ([[User talk:2A02:8109:40B:EF00:F805:A5D1:158:660B|talk]]) 14:37, 3 April 2025 (UTC)
:::That all natural numbers are finite comes from any straightforward definition of the natural numbers, such as the [[Peano axioms]]. It's not a question of what I allow or don't allow, and it's nothing to do with the size of the universe. [[User:MartinPoulter|MartinPoulter]] ([[User talk:MartinPoulter|talk]]) 14:50, 4 April 2025 (UTC)