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

On 16.11.2024 23:36, Jim Burns wrote:

On 11/16/2024 2:54 PM, WM wrote:

Therefore
the set of intervals cannot grow.

 An infinite set can match a proper superset
without growing.

But with shrinking. When it matches first itself and then a proper subset, then it has decreased. The set of even numbers has fewer elements than the set of integers.

Because it is infinite.

The interval [0, 1] is infinite because it can be split into infinitely many subsets. But its measure remains constant. There is no reason except naivety to believe that the intervals [n - 1/10,  n + 1/10] could cover the real line infinitely often.
Regards, WM