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

On 12/12/24 9:44 AM, WM wrote:

On 12.12.2024 13:26, Richard Damon wrote:

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:

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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].

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

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It is precisely this.

 

No, Cantors pairing is between two SETS, not a set and its subset.
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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.

 Both is the same. In emancipated version it is not as obvious as in the subset version.

Nope, when the subset is considered as its own independent set, the operation you want to do isn't part of its operations.

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By your logic, *NO* set can be infinite,

 False.

So, you admit that the proper subset can be equalinumerous to the parent set, even though there are members of the parent set that it doesn't contain?

 

as no proper subset can be equinumerous to its superset.

 Correct. You have got it!

Which mean you can't have infinite sets.

 Regards, WM