Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit String pairs

Am Thu, 31 Oct 2024 07:19:18 -0500 schrieb olcott:

On 10/31/2024 5:34 AM, Mikko wrote:

On 2024-10-30 12:16:02 +0000, olcott said:

On 10/30/2024 5:02 AM, Mikko wrote:

On 2024-10-27 14:21:25 +0000, olcott said:

On 10/27/2024 3:37 AM, Mikko wrote:

On 2024-10-26 13:17:52 +0000, olcott said:
>

Just imagine c functions that have enough memory to compute sums
and products of ASCII strings of digits using the same method that
people do.

Why just imagein? That is fairly easy to make. In some other
lanugages (e.g. Python, Javascript) it is alread in the library or
as a built-in feature.

OK next I want to see the actual Godel numbers and the arithmetic
steps used to derive them.

They can be found in any textbook of logic that discusses
undecidability.
If you need to ask about details tell us which book you are using.

Every single digit of the entire natural numbers not any symbolic name
for such a number.

Just evaluate the expressions shown in the books.

To me they are all nonsense gibberish. How one can convert a proof about
arithmetic into a proof about provability seems to be flatly false.

The key is selfreference. There is a number that encodes the sentence
"the sentence with the number [the number that this sentence encodes to]
is not provable".

It might be the case that one number fills 100 books of 1000 pages
each.

You fill find out when you evaluate the expressions. If you use Gödel's
original numbering you will need larger numbers than strictly
necessary. If you first encode symbols with a finite set of characters
you can encode everything with finite set of characters.

A book a trillion light years deep?

Is finite.

Then you can encode those character strings as integers. The number of
digits can be determined from the length of the character strings.
Besides, computations are much faster than with Gödel's powers of
primes.

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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.