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

On 04.12.2024 19:22, FromTheRafters wrote:

I like to look at it as {0,1,2,...} has a larger 'scope' of natural numbers than {1,2,3,...} while retaining the same set size. It does this by not being finite.

No, the sets of algebraic numbers and of prime numbers have very different sizes. The "bijection" holds only for such elements which have almost all elements remaining as successors. The latter cannot be paired. They always remain dark.
Contrary to that Cantor believed that all elements are in the bijection: "The infinite sequence thus defined has the peculiar property to contain the positive rational numbers completely, and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
Your belief is an incredible mass hysteria because it is so obviously wrong.
Regards, WM