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

On 20.12.2024 03:52, Richard Damon wrote:

On 12/19/24 10:47 AM, WM wrote:

On 19.12.2024 11:41, Mikko wrote:
>

Not really. What is acceptable for applied mathematics depends on the
application area, which you didn't specify.

>
It was obvious when the argument was discussed: The cursor moves from 0 to 1 on the real axis. For every unit fractions 1/n which it hits there are smaller unit fractions which it had not hit before because they were dark at the first time and came into being only later.

No, it means you missed them because you moved too far, because you closed your eyes.

The cursor moves until it hits a unit fraction.

This shows that you can't move to the "first" (smallest valued) 1/n because no such number actually exist,

But as soon the cursor has met a unit fraction, many smaller ones show up. They had nor "actually" existed as visible unit fractions.
Regards, WM