Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: Re: Turing computable function for sum of two integers Date: Wed, 30 Apr 2025 19:55:37 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <3f86781651b66cfa582c1cdf6657dd016b2d595d@i2pn2.org> References: <852f89c9196e0261b8156050fea4572fe886933f@i2pn2.org> <63af93cb608258cc3e12b9bab3a2efa0b7ee7eee@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 30 Apr 2025 23:56:03 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2600536"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird Content-Language: en-US In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 On 4/30/25 1:36 PM, olcott wrote: > On 4/29/2025 4:50 AM, Mikko wrote: >> On 2025-04-28 19:55:35 +0000, olcott said: >> >>> On 4/28/2025 11:01 AM, dbush wrote: >>>> On 4/28/2025 11:52 AM, olcott wrote: >>>>> On 4/28/2025 4:01 AM, Mikko wrote: >>>>>> On 2025-04-16 17:36:31 +0000, olcott said: >>>>>> >>>>>>> On 4/16/2025 7:29 AM, Richard Heathfield wrote: >>>>>>>> On 16/04/2025 12:40, olcott wrote: >>>>>>>>> sum(3,2) IS NOT THE SAME AS sum(5,2). >>>>>>>>> IT IS EITHER STUPID OR DISHONEST FOR YOU TO TRY TO >>>>>>>>> GET AWAY FOR CLAIMING THIS USING THE STRAW DECEPTION >>>>>>>>> INTENTIONALLY INCORRECT PARAPHRASE OF MY WORDS. >>>>>>>> >>>>>>>> Whether sum(3,2) is or is not the same as sum(5,2) is not the >>>>>>>> question. The question is whether a universal termination >>>>>>>> analyser can be constructed, and the answer is that it can't. >>>>>>>> >>>>>>>> This has been rigorously proved. If you want to overturn the >>>>>>>> proof you've got your work cut out to persuade anyone to listen, >>>>>>>> not least because anyone who tries to enter into a dialogue with >>>>>>>> you is met with contempt and scorn. >>>>>>>> >>>>>>>> The proof stands. >>>>>>>> >>>>>>> >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> *corresponding output to the input* >>>>>>> >>>>>>> Not freaking allowed to look at any damn thing >>>>>>> else besides the freaking input. Must compute whatever >>>>>>> mapping ACTUALLY EXISTS FROM THIS INPUT. >>>>>> >>>>>> A halt decider is is not allowed to compute "whatever" mapping. It is >>>>>> required to compute one specific mapping: to "no" if the computation >>>>>> described by the input can be continesd forever without halting, to >>>>>> "no" otherwise. >>>>>> >>>>> >>>>> It must do this by applying the finite string transformation >>>>> rules specified by the x86 language to the input to HHH(DD). >>>>> >>>>> This DOES NOT DERIVE THE BEHAVIOR OF THE DIRECTLY EXECUTED DD. >>>>> It DOES DERIVE DD EMULATED BY HHH AND ALSO DERIVES THE RECURSIVE >>>>> EMULATION OF HHH EMULATING ITSELF EMULATING DD. >>>>> >>>> >>>> >>>> In other words, no H exists that satisfies the following requirements, >>> >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >>> BECAUSE THOSE REQUIREMENTS HAVE ALWAYS BEEN WRONG AND NO ONE NOTICED. >> >> You have not proven that the requirements are wrong in any sense. >> > > int sum(int x, int y) { return 5; } > Is NOT a Turing Computable function for the sum of two integers. But it * > > int sum(int x, int y) { x + y; } > Is a Turing Computable function for the sum of two integers. > No, it is an algorithm in the C language to compute the Computable Function for addition. No algorithm/program is a "Function" in the computation theory sense of the word, that is just a category error. algorithms/programs COMPUTE Functions, which are just the complete mapping of inputs to outputs that the Function Defines. Being Computable just means that an algorithm/program exists that computes it. Perhaps you need to go back to Freshman Programming to learn the meanings of the words you are misusing.