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

On 23.12.2024 01:05, FromTheRafters wrote:

WM brought next idea :
>

The function E(n) decreases from infinity to zero because in set theory ℕ \ {1, 2, 3, ...} =  { } is an accepted formula.

 In what way is it decreasing?

One by one. Every endsegment transforms a natural number from content inside to index outside. That is guaranteed by mathematics:
∀k ∈ ℕ : ∩{E(0), E(1), E(2), ..., E(k+1)} = ∩{E(0), E(1), E(2), ..., E(k)} \ {k+1}. Note the universal quantifier.
Regards, WM