Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 22.01.2025 13:10, Richard Damon wrote:

On 1/22/25 5:36 AM, WM wrote:

On 22.01.2025 00:41, Richard Damon wrote:

On 1/21/25 7:48 AM, WM wrote:

On 21.01.2025 13:17, Richard Damon wrote:
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the matching happens as a collective whole. It can't complete if you don't move from the individual step to the collective step.

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So it is.
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And thus,

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there are visible and dark numbers. As you said: We have to move from the individual step to the collective step.
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But the numbers being used didn't change, only the logic.

Numbers do not change. Only their state of being known.

 I guess when we talk about the set { 0, 1, 2, 3, ... } you must be defining "4" as a "dark number" as that was the point we shifted from listing them individually to collectively.

No. Every number that is defined in a system by its FISON is visible. Many numbers smaller than 10^99 are defined on the pocket calculator. No greater number can be defined in that system.

 The basic problem with your "dark numbers" is that no number itself is "dark", the collective nature is just how we chose to use that number.

It is how we *can* chose them.
Regards, WM