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

On 12/13/24 3:42 AM, WM wrote:

On 13.12.2024 03:29, Richard Damon wrote:

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.

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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.

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

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

 The subset is considered as its own independent set D = {10n | n ∈ ℕ} and then it is attached to the set ℕ = {1, 2, 3, ...}. R´That does not change the subset.
 Regards, WM
 

What is this "attached" operation you are talking about?
How does it affect the pairing of each 10n in D to n in N?
Where did the pairing go wrong?
Which number in N failed to have it pair BY THAT PAIRING to a value in D?