Re: Replacement of Cardinality

On 8/3/24 10:30 AM, WM wrote:

Le 02/08/2024 à 19:08, Richard Damon a écrit :

On 8/2/24 12:32 PM, WM wrote:

 

Note: For every 1/n there exists a smaller real number. But they cannot be chosen because most 1/n already cannot be chosen. Proof: For every chosen eps you fail to separate infinitely many unit fractions.

>
WHY CAN'T IT BE CHOSEN?

 Because it is dark.

Why is it dark, we know a possible value for it, and thus can choose it.
You just incorrectly assume that some numbers just can't be reached because some 'magic" made them dark.
No, your dark numbers are non-finite numbers that you invent to try to explain why your logic doesn't work with unbounded numbers.

 

If there WAS just a single eps that seperated ALL unit fractions, then the could be no more than 1/eps unit fractions,

 But there is not even an eps that separates half of all unit fractions.

Because such a question is meaningles, as there isn't a finite number that is half of the count of unit fractions.
This is the problem with your logic, it doens't understand that the size of the unbounded set isn't a finite number that you can do normal math with.

 Regards, WM