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

On 1/9/25 7:37 AM, WM wrote:

On 09.01.2025 02:26, Richard Damon wrote:

On 1/8/25 5:06 PM, WM wrote:

 

The set {1, 2, 3, ...} is smaller by one element than the set {0, 1, 2, 3, ...}. Proof: {0, 1, 2, 3, ...} \ {1, 2, 3, ...} = {0}. Cardinality cannot describe this difference because it covers only mappings of elements which have almost all elements as successors.
>

But Alelph_0, the size of the second, is also the size of the first, as Aleph_0 - 1 is Aleph_0.

 As I said, cardinality cannot describe this difference of one element.
 Regards, WM

Because the property that "cardinality" describes doesn't have that difference.
It is only in your IGNORANCE that you think the two sets have different size,
You would need to go to some trans-trans-finite mathematics to handle that mathematics. Since you don't think that even "normal" infinity can exist, that is beyond your thinking.
Sorry, but your logic is just going super-nova and leaving you in total and utter darkness by its contradictions.