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

Am 28.12.2024 um 06:28 schrieb Moebius:

Am 28.12.2024 um 06:23 schrieb Moebius:

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

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all FISONs contain/are all n.

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Mumbo-jumbo.
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Hint: For each and every n e IN there is a FISON such that n is in it.
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BUT there's no FISON such that each and every n e IN is in it.

 Mückenheim: "all singletons contain/are all n".
 Hint: For each and every n e IN there is a singleton such that n is in it (namely {n}).
 BUT there's no singleton such that each and every n e IN is in it.
 <facepalm>

On the other hand, _the UNION of_ all FISONs contains all n e IN.
In the same way, _the UNION of_ all "IN-singletons" contains all n e IN.
Using symbols: U_(n e IN) {m e IN : m < n} = IN and U_(n e IN) {n} = IN.
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