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

On 12/9/24 8:04 AM, WM wrote:

On 09.12.2024 13:03, Richard Damon wrote:

On 12/9/24 4:04 AM, WM wrote:

On 08.12.2024 19:01, Jim Burns wrote:
>

You (WM) are considering
infinite dark.finite.cardinals,
which do not exist.
>

Then analysis is contradicted in set theory.
∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
The limit of the left-hand side is empty, the limit of the right-hand side is full, i.e. not empty.
I do not tolerate that.
>

By your logic, 1 equals 0,

 No, that are two different sequences.
 Regards, WM
 

But since both 0^x and x^0 as x approaches 0 approach 0^0, your logic says that 0^0 is both 0 and 1.
Just because you have a sequence, doesn't mean you can talk about the end infinite state at the "end" of the sequence.
That is EXACTLY the logic you are trying to use, you have two sequences that seem to go to the same infinte set at the end, and these both seem to result in different values when they are only treated as finite sequences.
Thus, your "logic" also shows that 1 == 0, and thus your logic has blown itself up.