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

Am Thu, 09 Jan 2025 22:59:16 +0100 schrieb WM:

On 09.01.2025 21:19, joes wrote:

Am Thu, 09 Jan 2025 17:59:07 +0100 schrieb WM:

 

Are the natural numbers fixed or do they evolve?

Neither

There is no third alternative.

They are neither finite in number

Gibberish.
Are the natural numbers fixed or do they evolve?

Now this is gibberish. What do those terms mean? Are you referring
to their value, or to the set, or its size? You will find the
answers to be obvious.

The set of prime numbers is infinite but smaller because it is a
proper subset. It has less than 1 % content.

Any special reason for that figure?

It is vivid and true - the characteristic feature of my lectures.

And wrong. A good teacher should not pick an arbitrary number
as if it had any significance, lest alert listeners might wonder
if the sentence were true for that value only.

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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.