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

On 06.11.2024 12:46, Richard Damon wrote:

On 11/5/24 7:34 AM, WM wrote:

On 05.11.2024 13:03, Richard Damon wrote:

On 11/5/24 3:45 AM, WM wrote:

>

I describe that a point between two finite intervals has two finite intervals around it. Even this simple conclusion must be denied by the believers in matheology.

>

If you mean that between to finite length intervals, which include there endpoints, and a point that is between those two intervals, then YES there exist two other intervals between the point and those two intervals.

>
These other intervals also have irrational endpoints. Every point outside of an interval is next to some endpoint which is irrational.

 Or rational endpoints.

No, the rationals are centres of their intervals.

 There is no "next to" on the dense line

Every positive point is nearer to zero than to any negative point.
Of -x and 0 the latter is next to any positive x.
Regards, WM