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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit
 String pairs
Date: Thu, 31 Oct 2024 07:19:18 -0500
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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.

>> 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?

> 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.
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer