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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit
 String pairs
Date: Thu, 31 Oct 2024 13:58:31 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
Message-ID: <a5b9623eda10363c48629af3716975731d938a13@i2pn2.org>
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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.
-- 
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.