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Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail 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 Organization: A noiseless patient Spider Lines: 56 Message-ID: <vfvsk6$2mcse$3@dont-email.me> References: <ves6p1$2uoln$1@dont-email.me> <87634d01e18903c744d109aaca3a20b9ce4278bb@i2pn2.org> <vev8gg$3me0u$1@dont-email.me> <eb38c4aff9c8bc250c49892461ac25bfccfe303f@i2pn2.org> <vf051u$3rr97$1@dont-email.me> <e3f28689429722f86224d0d736115e4d1895299b@i2pn2.org> <vf1hun$39e3$1@dont-email.me> <dedb2801cc230a4cf689802934c4b841ae1a29eb@i2pn2.org> <vf1stu$8h0v$1@dont-email.me> <592109c757262c48aaca517a829ea1867913316b@i2pn2.org> <vf37qt$fbb3$1@dont-email.me> <vf5430$sjvj$1@dont-email.me> <vf5mat$v6n5$4@dont-email.me> <vf7jbl$1cr7h$1@dont-email.me> <vf8b8p$1gkf5$3@dont-email.me> <vfa8iu$1ulea$1@dont-email.me> <vfassk$21k64$4@dont-email.me> <vfdjc7$2lcba$1@dont-email.me> <vfdlij$2ll17$1@dont-email.me> <vffj9k$33eod$1@dont-email.me> <vfg6j4$36im7$1@dont-email.me> <vfi7ng$3kub8$1@dont-email.me> <vfiq60$3ner2$3@dont-email.me> <vfku48$78d0$1@dont-email.me> <vfli96$fj8s$2@dont-email.me> <vft079$23tm3$1@dont-email.me> <vft822$25aio$2@dont-email.me> <vfvmep$2lf25$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 31 Oct 2024 13:19:19 +0100 (CET) Injection-Info: dont-email.me; posting-host="a20cf42bc93637678342112c0763e5cc"; logging-data="2831246"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+piZah/XYjM/nmUIRRNf6k" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:sQFYxfWeaAT9Sp4LQM2nF4Vc1VM= Content-Language: en-US In-Reply-To: <vfvmep$2lf25$1@dont-email.me> X-Antivirus-Status: Clean X-Antivirus: Norton (VPS 241031-2, 10/31/2024), Outbound message Bytes: 4072 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