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

On 10.12.2024 01:45, Richard Damon wrote:

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.

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.

You should check your "logic". When two different sequences have different limits, this does not mean that the limits are identical. By the way 0^0 = 1 is simply a definition.

 Just because you have a sequence, doesn't mean you can talk about the end infinite state at the "end" of the sequence.

The end infinite state is a set.

  you have two sequences that seem to go to the same infinte set at the end,

Two sequences that are identical term by term cannot have different limits. 0^x and x^0 are different term by term.
REgards, WM