Re: Incompleteness of Cantor's enumeration of the rational numbers

Am Wed, 20 Nov 2024 19:37:20 +0100 schrieb WM:

On 20.11.2024 19:12, joes wrote:

Am Wed, 20 Nov 2024 17:51:19 +0100 schrieb WM:

On 20.11.2024 15:15, FromTheRafters wrote:

WM explained on 11/20/2024 :

set theory claims that all natural numbers can be counted to such
that no successors remain.

No it doesn't.

Even all rationals and algebraics.
"we get the epitome (ω) of all real algebraic numbers [...] and with
respect to this order we can talk about the nth algebraic number where
not a single one of this epitome has been forgotten"
"The infinite sequence thus defined has the peculiar property to
contain the positive rational numbers completely, and each of them
only once at a determined place"

You are once again lacking in precision:

It was Cantor who said the above. There is no lack of precision.

You misunderstood him. I don't see anything about successors.

every natural is finite and thus countable.

According to Cantor there is no number missing, let alone infinitely
many.

Numbers "missing" is meaningless. What did you mean to say here?

Set theory claims that all natural numbers can be counted to such
that no successors remain. That is false.

Obviously. There is no end to the successors such that you are done
counting them after some finite number.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.