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

On 18.11.2024 20:22, Jim Burns wrote:

The set of even numbers is
a proper subset of the set of integers,
AND
the set of even numbers can match
the set of integers without either set changing.

That implies that our well-known intervals can cover the real line or reduce the average covering to 1/1000000000.
But every finite translation of any finite subset of intervals maintains the relative covering 1/5. If the infinite set has the relative covering 1 (or more or less), then you claim that the sequence 1/5, 1/5, 1/5, ... has limit 1 (or more or less).
So you deny analysis or / and geometry.
Regards, WM