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

On 03.12.2024 01:32, Jim Burns wrote:

On 12/2/2024 9:28 AM, WM wrote:

 

A quantifier shift tells you (WM) what you (WM) _expect_
  but a quantifier shift is untrustworthy.

Here is no quantifier shift but an identity:

E(1), E(2), E(3), ...
and E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
are identical for every n and in the limit because E(1)∩E(2)∩...∩E(n)
= E(n).

 

No.
For the set of finite cardinals,
EVEN IF NO END.SEGMENT IS EMPTY,
  the intersection of all end segments is empty.

I cannot read or understand the above. The following is gibberish.

⎜ EVEN IF NO END.SEGMENT IS EMPTY,
⎝  the intersection of all end segments is empty.

E(1)∩E(2)∩...∩E(n) = E(n).
Sequences which are identical in every term have identical limits.