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Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail 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 Organization: - Lines: 62 Message-ID: <vg24e8$3618s$1@dont-email.me> References: <ves6p1$2uoln$1@dont-email.me> <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> <vfvsk6$2mcse$3@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 01 Nov 2024 09:44:56 +0100 (CET) Injection-Info: dont-email.me; posting-host="7e2b82ca9029ad469da0f8351daaed7e"; logging-data="3343644"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/SgETgSfWfNxOF6Hfmppkn" User-Agent: Unison/2.2 Cancel-Lock: sha1:/OR1wWuodYQGry6P+1bvz8xtapg= Bytes: 3951 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