Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/29/2024 2:37 PM, WM wrote:

On 29.11.2024 19:08, Jim Burns wrote:

After all the swaps
 (of which no swap is a change in cardinality)
what remains is a proper subset
 (which is not a change in cardinality).

>
Not proper.

Proper.
The sets
  are larger than
   each cardinal which can change by 1
  have a cardinal which cannot change by 1
The proper subset has the same cardinality.

No element can leave by swaps.

All the swaps match all the elelments of that set
and all the elments of that proper subset.
No elements leave.

 (which is not a change in cardinality).

>
Irrelevant. Cardinality is a fuzzy measure.

The whole ℕᶠⁱⁿ×ℕᶠⁱⁿ matrix can fit in
its first column ℕᶠⁱⁿ×{0}
The fuzzy cardinality property
  predicts that it can.
Your crisp cardinoid property
  predicts otherwise
  and is incorrect.
After all the swaps
  (of which no swap is a change in cardinality)
what remains is a proper subset
  (which is not a change in cardinality).
'Bye, Bob.