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

On 05.01.2025 12:28, Alan Mackenzie wrote:
 

The only people who talk about "potential" and "actual" infinity are
non-mathematicians who lack understanding, and pioneer mathematicians
early on in the development of set theory who were still grasping after
precise notions.

  All mathematicians whom you have disqualified above are genuine mathematicians.
 What you perhaps could understand is this simple example: As Cantor said actual infinity, for instance omegas and alephs and ℕ are fixed quantities. The set ℕ is invariable. But all finite initial segments of natural numbers FISONs {1, 2, 3, ..., n} cover less than 1 % of ℕ. Proof: {1, 2, 3, ..., 100n} is less than ℕ. That means the set of FISONs will never cover ℕ, nor will its union reach the invariable quantity. The set of FISONs is only potentially infinite, not a fixed quantity but growing over all finite bounds.