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

On 12/19/2024 6:58 AM, WM wrote:

On 19.12.2024 04:29, Richard Damon wrote:

On 12/18/24 2:06 PM, WM wrote:

On 18.12.2024 13:29, Richard Damon wrote:

On 12/17/24 4:57 PM, WM wrote:

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You claimed that he uses more than I do, namely all natural numbers.

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Right, you never use ALL the natural numbers, only a finite subset of them.

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Please give the quote from which you obtain a difference between
"The infinite sequence thus defined has the peculiar property to contain the positive rational numbers completely, and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
and my "the infinite sequence f(n) = [1, n] contains all natural numbers n completely, and each of them only once at a determined place."
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How is your f(n) an "infinite sequence, since n is a finite number in each instance.

 How is Cantor's sequence infinite since every positive rational number is finite?

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NONE of your f(n) contains *ALL* natural numbers, since no "n" is the highest natural number,

Cantor Pairing does not deal with rationals. It can create a unique pair of unsigned integers from any unsigned integer. Then we can use that unique pair to go back to the original unsigned integer.

 None of Cantor's terms q_n contains all rational numbers, sice no n is the highest natural number.
 

Your problem is you just don't understand what "infinity" is

 Your problem is that you believe to understand it.
 Regards, WM