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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit
 String pairs
Date: Thu, 31 Oct 2024 19:08:51 -0400
Organization: i2pn2 (i2pn.org)
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On 10/31/24 8:19 AM, olcott wrote:
> 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.

And to assert that just because something seems "gibberish" to you means 
it is false, just proves that you don't undetstand how logic works.

> 
>>> 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?

Maybe, but that isn't important to the proof.

> 
>> 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.
>>
> 
>