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

On 1/9/2025 5:15 PM, Moebius wrote:

Am 09.01.2025 um 22:12 schrieb Chris M. Thomasson:

On 1/9/2025 8:18 AM, WM wrote:

On 09.01.2025 10:56, FromTheRafters wrote:

WM explained :

>

The set {1, 2, 3, ...} is smaller by one element than the set {0, 1, 2, 3, ...}.

>
Both sets are equal in size

>
No. Both sets appear equal (although everybody can see that they are not) when measured by an insufficient tool.

>
{ 0, 1, 2, 3, ... } = { 1 - 1, 2 - 1, 3 - 1, 4 - 1, ... }

 Really? :-)
 

Well, wrt their elements are equal to each other. Fair enough?
;^o
{ 0, 1, 2, 3, ... } = { 1 - 1, 2 - 1, 3 - 1, 4 - 1, ... }
where:
{ 0 = 1 - 1, 1 = 2 - 1, 2 = 3 - 1, 3 = 4 - 1, ... }
? Kind of okay? They both have the same number of elements.