Re: Simple enough for every reader?

On 03.06.2025 10:11, Mikko wrote:

On 2025-06-01 14:09:23 +0000, WM said:
 

On 01.06.2025 13:58, Mikko wrote:

On 2025-05-31 13:47:51 +0000, WM said:
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On 31.05.2025 12:11, Mikko wrote:

On 2025-05-30 14:46:55 +0000, WM said:
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{1, 2, 3, ..., n, n+1} has infinitely many (ℵo) successors is a consequence of {1, 2, 3, ..., n} has infinitely many (ℵo) successors, and ℵo - 1 = ℵo.

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Still no proof.

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Proof that every definable natural number has more successors than predecessors.

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You have not shown that proof, either.

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I have above. You cannot understand it. That is a different thing.

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No proof of anything above. Besides, nothing that requires any
understanding beyond ordinary proof checking cannot be a proof.

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There is no further understanding required.

 That contradicts your above "You cannot understand it".

No, ordinary proof checking and your understanding are two different things.
Every proof checker can confirm that every definable natural number has finitely many predecessors. If there are more than finitely many numbers following upon every definable number as successors, then every definable number has more successors than predecessors.
All can be removed collectively. ℕ \ {1, 2, 3, ...} = { }.
If all could be removed as individuals, then a last one would be removed. Contradiction.
This is a proof of dark natural numbers.
Regards, WM