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

On 12/12/24 4:53 AM, WM wrote:

On 12.12.2024 01:38, Richard Damon wrote:

On 12/11/24 9:04 AM, WM wrote:

 

In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. [Wikipedia].

 

So? That isn't what Cantor was talking about in his pairings

 It is precisely this.
 Regards, WM
 

No, Cantors pairing is between two SETS, not a set and its subset.
Yes, we can call the subset a set, since it is, but then when we look at it for the pairing, we need to be looking at its emancipated version, not the version tied into the original set.
By your logic, *NO* set can be infinite, as no proper subset can be equinumerous to its supeerset.
That is exactly one of the flaws of your logic, it can't deal with the infinite.
Sorry, you lose.