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

On 12/28/24 8:48 AM, WM wrote:

On 28.12.2024 06:23, Moebius wrote:

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On 12/17/24 4:51 PM, WM wrote:

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all FISONs contain/are all n.

 

Hint: For each and every n e IN there is a FISON such that n is in it.

 No. If so, then the union of all FISONs would contain all n. But fact is that the union of all FISONs is a FISON (all FISONs have infinitely many successors) and leaves almost all numbers outside
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
 Regards, WM

No, doing an INFIITE union (which a union of all FISONs would be) can result in something different in type then the union of a finite number of FISONs.
Just like the combining of ALL natural numbers gives us an infinite set, while ony combining a finite number of natural numbers gives us a finite set.
You logic just can't handle infinite operations, and thus can't actually have the set of Natural Numbers as an element of it,