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

On 12/10/24 12:30 PM, WM wrote:

On 10.12.2024 13:17, Richard Damon wrote:

On 12/10/24 3:50 AM, WM wrote:

 

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

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Which isn't the part I am talking of, it is that just because each step of a sequence has a value, doesn't mean the thing that is at that limit, has the same value.

 Of course not. But if each step of two sequences has the same value, then the limits are the same too. This is the case for
  (E(1)∩E(2)∩...∩E(n)) and (E(n)).
 Regards, WM
 

But the limit of the sequence isn't necessary what is at the "end" of the sequence.
That is exactly the problem of 0^x and x^0, both get you to the same point, but with different values, so we can't use limits to necessarily determine what is the value of that point.