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

On 11/29/2024 4:23 PM, WM wrote:

On 29.11.2024 21:37, Jim Burns wrote:

On 11/29/2024 2:41 PM, WM wrote:

On 29.11.2024 19:53, Jim Burns wrote:

all fall out == empty

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== empty endsegment.

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No.
Empty intersection of all and only infinite end.segments.

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All natnumbers fall out of the endsegmets

Each finite.cardinal k is countable.past to
  k+1 which indexes
   Eᶠⁱⁿ(k+1) which doesn't hold
    k which is not common to
     all end segments.
Each finite.cardinal k is not.in
  the set of elements common to all end.segments,
  the intersection of all end segments,
   which is empty.
No numbers are remaining.

but the endsegments keep infinitely many natnumbers.

For each end.segment of finite.cardinals,
for each finite cardinal,
that end.segment has a subset larger than that cardinal.
Each end.segment of finite.cardinals
does not have any finite cardinality
is infinite.

Can a stronger nonsense exist?
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infinite and empty

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According to set theory.

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You imagine that's what set theory says.
It doesn't say that.

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It does say that
infinite endsegments have an empty intersection
because all natnumbers fall out of the endsegments.

Each finite cardinal is not.in
at least one end.segment of the finite.cardinals.

Where else could they fall out?

The end.segments are infinite.
Their intersection is empty.
No end.segment is their intersection.
Nothing is infinite and empty.