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

On 12/19/24 9:58 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?

Because there is an infinite number of numbers.

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

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

??? Where does Cantor assume there is a highest n?
He builds an infinite sequence that pairs a netual number to every rational number .Actualy to every number pair, so every rational number get paired to many natural number showing that the rationals can not be bigger than the Naturals. But since every Natural Number is a rational, there can't be more Natural Nubmers than Rational Numbers, so we can show they must be the same size.

 

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

 Your problem is that you believe to understand it.

In other words you ADMIT you don't understand what you are talking about?
Glad you are honest about your dishonesty,

 Regards, WM