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

On 12/15/24 2:29 PM, WM wrote:

On 15.12.2024 13:52, Richard Damon wrote:

On 12/15/24 6:05 AM, WM wrote:

 

You believe that only afterwards the first interval comes into being?
That is not the infinity used in set theory.

 

There is no "next", only before or after in dense sets.
>
Next is a property of directly indexed sets

 Next is a geometric property, in particular since the average distance of intervals is infinitely larger than their sizes.
 Regards, WM

Nope. Next is a property of SEQUENCE.
Not sure where you get that the "average" distance of intervals is infinitely larger than ther sizes. If you allow skippping over other intervals, maybe, but then you are not looking at what you are trying to talk about.
To have a "next" point, there needs to be a point for which no other point can be between the given one and that one. Since we have more points between any two points, we don't have "next".
Your math is using the same error that shows that 0 == 1.