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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit String pairs
Date: Thu, 31 Oct 2024 12:34:01 +0200
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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.

> 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. 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.

-- 
Mikko