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.

You 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.
Regards, WM