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

Am Mon, 30 Dec 2024 22:53:38 +0100 schrieb WM:

On 30.12.2024 21:28, joes wrote:

Am Mon, 30 Dec 2024 09:40:11 +0100 schrieb WM:

 

FISONs do not grow by unioning them. All FISONs and their unions stay
below 1 % of ℕ.

Even better, they are finite (but they do grow).

They do grow but will never surpass 1 % of ℕ.

 

Proof: Every FISON that is multiplied by 100 remains a FISON that can
be multiplied by 100 without changing this property.

Do you mean the set of numbers less than 100n? I thought you didn’t
believe in the closure of N under multiplication.

The collection of natural numbers is closed under multiplication.In fact
it will ever reach let alone surpass any definable fraction of ℕ.

WTF? N *is* the set(!) of natural numbers, and it is infinite.
Now what is the multiplication of a FISON?

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.