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

On 11/26/24 9:02 AM, WM wrote:

On 26.11.2024 14:11, Richard Damon wrote:

On 11/26/24 6:05 AM, WM wrote:

On 26.11.2024 10:08, Mikko wrote:

On 2024-11-25 13:55:57 +0000, WM said:

>

But before touching a rational it will touch an irrational.

>
Of course as the starting point is outside of all the intervals and
every rational is in some of the intervals and therefore must be
irrational. But when it has moved to another point it has already
moved over both infinitely many irrationals

>
This is true in every case. The intermediate numbers cannot be discerned. They are dark. This is so in fact between every pair of discernible real numbers: There are infinitely many dark numbers between them.

 

Name a pair of numbers that you can not see one of the numbers between them.

 Between every pair of discernible real numbers potentially infinitely many real numbers can be seen. But between seen numbers there are always actually infinitely many dark numbers which cannot be seen

No, your problem is that you THINK there are dark numbers, but you don't understand that all of them are able to be seen, you just close your eyes to them because your brain can't handle them.

>
All you have done is shown that to you *ALMOST* *ALL* numburs are "dark" because your logic can't handle them,

 Neither can you.

I don't need to understand "dark" numbers, as I know they are just part of your fiction.

 

even though the mathematics that defines them fully defines them so others CAN handle them.

 It defines the set but not its individual elements.

Sure it does. What number exists that it can not define?

>
Your "darkness" is just you closing your eyes to the contradictions that you invalid use of finite logic on an infinite set

 All logic is finite.

But some logic can handle infinite sets, by not assuming the set is finite.
That is your problem, you can't think of something bigger than you because you have blown up your imagination.

 Regards, WM