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

On 1/15/25 1:13 PM, WM wrote:

On 14.01.2025 19:41, Jim Burns wrote:

On 1/14/2025 4:07 AM, WM wrote:

On 13.01.2025 20:31, Jim Burns wrote:

On 1/13/2025 12:17 PM, WM wrote:

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A step is never from finite to infinite.

 The dark realm is appears infinite.

There is no infinite set smaller than ℕ
#𝔼 ≥ #ℕ

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That is obviously wrong.

  The rule of subset proves that every proper subset has fewer elements than its superset. So there are more natural numbers than prime numbers, || > ||, and more complex numbers than real numbers, || > ||. Even finitely many exceptions from the subset-relation are admitted for infinite subsets. Therefore there are more odd numbers than prime numbers || > ||.

Which doesn't apply to infinite sets.
Where are you getting your broken rules from.

  The rule of construction yields the number of integers || = 2|| + 1 and the number of fractions || = 2||2 + 1 (there are fewer rational numbers # ). Since all products of rational numbers with an irrational number are irrational, there are many more irrational numbers than rational numbers || > |#|.

Yes, there are more irrational numbers thn rational numbers,

  The rule of symmetry yields precisely the same number of real geometric points  in every interval (n, n+1] and with at most a small error same number of odd numbers and of even numbers in every finite interval and in the whole real line.
 

There is no infinite set smaller than ℕ.

 {2,3, 4, ...} is smaller by one element.

Which, since that size is infinite, is the same size.
A fact you don't seem to be able to understand, since your mind is stuck in finite arithmatic,

 Regards, WM