Re: Incompleteness of Cantor's enumeration of the rational numbers

On 12/22/24 10:04 AM, WM wrote:

On 22.12.2024 13:28, Richard Damon wrote:

On 12/21/24 4:40 PM, WM wrote:

 

The reason is that after every visible unit fraction there are more visible unit fractions created. That is potential infinity. You can't understand that matter.

>
No, they are not "created" they have always been there, they just haven't been enumerated/discovered yet.

 Why haven't they?

Because you just haven't had time to discover it, because you are a finite entity.
A finite universe can only describe a finite number of finite number, but the mathematical set of the natural numbers goes beyond that.
Your problem seems to be that your brain just can't handle the abstract.

The numbers didn't just show up, they were always there and we didn't do anything that prohibited it from stopping at any of them.

>
They were dark.

>
No, you just didn't see them because your logic closes its eyes and lies to you.

 Then show me a unit fraction that you see for the first time when going from 0 to 1 which has no smaller unit fractions that you hadn't discovered before.
 

But the question isn't "hadn't discovered befor" but which exists. An there isn't a "first" unit fraction on the line from that end, because the set is unbounded, so asking about where something that doesn't exist would be is just an invalid question.
YOU are the one that needs to show that such a number exists, as such a number is REQUIRED to exist to use your logic, and not just one that hadn't been discovered before, but isn't defined as a potential number of the set.
Since you can't do that, and seem to be admitting it, you are just admitting that you logic is just broken and you logic worthless. Your logic is based on "facts" that can't be seen, and thus are not actually "facts" but just misconceptions that have formed the black hole that sucks in all your logic and leaves your brain in darkness.

Regards, WM