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

On 1/5/25 12:04 PM, WM wrote:

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.
 Regards, WM
 

And this logic just shows that YOU are not actually a mathematicians, but a idiot trying to follow superstitious fallacies about mathematics.
You just don't undetstand the actual meaning of the words you use, but try to redefine them to non-sense, as that is all you understand.
You are just too stupid to understand that the *INFINITE* set of FISONs (all of which are finite) does reach that which you say it can't, but the reason it can is just beyound your idiotic ability to comprehend, and you instance that your logic works just proves your utter stupidity.
YOU BRAIN IS JUST TOO SMALL TO HANDLE THE CONCEPTS, and likely never can get there. That doesn't mean the concepts are wrong, but that YOU are the one that is wrpng to talk about things you don't understand, while claiminig you do.
Sorry, but all you are doing is proving your stupid, so stupid you think you are smart. Perfect example of Dunning-Kruger.