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

On 1/10/25 11:19 AM, WM wrote:

On 10.01.2025 13:41, Richard Damon wrote:

On 1/9/25 7:37 AM, WM wrote:

 

As I said, cardinality cannot describe this difference of one element.

 

Because the property that "cardinality" describes doesn't have that difference.

 So it is. Cardinality cannot describe the difference of one element, not even of infinitely many. Infinite is simply infinite, no matter what the real size is.

Cardinality CAN describe the difference of one element, if the sets are finite.
And Infinite isn't just Infinite, as there *ARE* graduations in it. The number of Real Numbers is bigger than the Number of Natural Numbers or Rational Numbers. Your logic just can't handle that fact, because it can't handle any infinite thing.

 You need not understand that. But the claim that different sets like ℕ and ℚ are of same size shows that you have been stultified by set theory.
 

No, the fact that you refuse to beleive what is proven show that you are just too stupid to understand set theory.
And, the fact that you can't even formally define how your logic actually works, just shows how failed your idea of "logic" is.
You say that the classical set theory doesn't work, but your only argument is based on a "logic" that can show that 0 == 1, so is proven to be fundamentally flawed.
YOU are the one that is ignorant and out of touch.

Regards, WM