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

On 12/9/24 9:40 AM, WM wrote:

On 08.12.2024 21:22, joes wrote:

Am Tue, 03 Dec 2024 12:10:53 +0100 schrieb WM:

On 03.12.2024 11:03, Mikko wrote:
>

I understand mathematics

Hardly, though you may have the impression.
Proof: You cannot understand that the function f(10n) = n from D = {10n
| n ∈ ℕ} to ℕ = {1, 2, 3, ...} is not a bijection because for every
initial segment {1, 2, 3, ..., n} of ℕ there are too few numbers of the
form 10n that can be paired with numbers n.

Wow. For every segment there are numbers {10, 20, …, 10n}.

 But for every segments more are needed: {1, 2, 3, ..., 10n}
 Regards, WM
 

but {1, 2, 3, ..., 10n} would have its pairing with the set
{10, 20, 30, ... 100n}
The pairing is between TWO sets, not the members of a set with itself.