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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: Fri, 1 Nov 2024 10:44:56 +0200
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On 2024-10-31 12:19:18 +0000, olcott said:

> 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.

The books define everything needed in order to understand the encoding
rules.

Encoding nonsense gibberish as a string of digits is trivial.

> How one
> can convert a proof about arithmetic into a
> proof about provability seems to be flatly false.

You needn't. The proof about provability is given in the books so
you needn't any comversion.

>>> 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?

The number of digits in a Gödel number can be computed with less effort
than the Gödel number itself. Still easier to compute a rough estimate.

-- 
Mikko