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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: Turing Machine computable functions MUST apply finite string transformations to inputs Date: Wed, 30 Apr 2025 22:50:47 -0500 Organization: A noiseless patient Spider Lines: 88 Message-ID: References: <87cyd5182l.fsf@nosuchdomain.example.com> <991dde3a60e1485815b789520c7149e7842d18f2@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 01 May 2025 05:50:47 +0200 (CEST) Injection-Info: dont-email.me; posting-host="426e05277e8812ec523191f9693f8994"; logging-data="1914998"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/E9NJ01QVr+Pvwgbf/UvzP" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:k6J8CQnGXZKzyGYP5zw92z1VB1A= In-Reply-To: X-Antivirus: Norton (VPS 250430-10, 4/30/2025), Outbound message X-Antivirus-Status: Clean Content-Language: en-US Bytes: 5162 On 4/30/2025 7:17 PM, André G. Isaak wrote: > On 2025-04-30 16:09, olcott wrote: >> On 4/30/2025 2:55 PM, dbush wrote: >>> On 4/30/2025 1:32 PM, olcott wrote: >>>> On 4/30/2025 11:11 AM, Richard Heathfield wrote: >>>>> On 30/04/2025 16:44, joes wrote: >>>>>> Am Wed, 30 Apr 2025 10:09:45 -0500 schrieb olcott: >>>>>>> On 4/29/2025 5:01 AM, Mikko wrote: >>>>>> >>>>>>>> Irrelevant. There is sufficient agreement what Turing machines are. >>>>>>> >>>>>>> Turing machine computable functions must apply finite string >>>>>>> transformation rues to inputs to derive outputs. >>>>>>> >>>>>>> This is not a function that computes the sum(3,2): >>>>>>> int sum(int x, int y) { return 5; } >>>>>> Yes it is, for all inputs. >>>>> >>>>> Not much of a computation, though, is it? >>>>> >>>> >>>> It IS NOT a Turing Computable function >>> >>> Lying by misuse of terms. >>> >>> A turing computable function is a mapping for which an algorithm >>> exists to compute it, not the algorithm itself. >>> >>> Further use of "turing computable function" when what is meant is >>> "algorithm" will result in the former being replaced with the later >>> in future responses to your posts to make it clear what you are >>> actually talking about. >>> >>> >>>> because it does not ever apply any finite >>>> string transformation  rules to its inputs. >>> >>> Sure it does.  It computes the mapping of all pairs of integers to >>> the number 5. >>> >> >> int sum(int x, int y) { return 5; } >> Does not apply transformations to its inputs >> to derive its outputs thus is no kind of computable >> function not even for sum(2,3). > > You are still hopelessly confused about your terminology. > > Computable functions are a subset of mathematical functions, and > mathematical functions are *not* the same thing as C functions. > Functions do not apply "transformations". They are simply mappings, and > a functions which maps every pair of natural numbers to 5 is a perfectly > legitimate, albeit not very interesting, function. > > What makes this function a *computable function* is that fact that it is > possible to construct a C function (or a Turing Machine, or some other > type of algorithm) such as int foo(int x, int y) {return 5;} which > computes that particular function; but the C function and the computable > function it computes are entirely separate entities. computes the sum of two integers by transforming the inputs into an output. int sum(int x, int y) { return x + y; } Computes no function because it ignores its inputs. int sum(int x, int y) { return 5; } > [I won't call that > function 'sum()' because that would be misleading, but the the *name* > assigned to a C function has no necessary relation to the function it > computes. It's good programming practice to give functions descriptive > names but nothing in the C standard requires it). > > You keep conflating C functions/Turing Machines with computable > functions and as a result come across as completely ignorant about the > topic you purport to be discussing. No C function or Turing Machine is a > computable function. They are ways of expressing algorithms. > > André > The complete ignorance is to expect HHH(DD) to report on DD(DD). That is just not the way that reality works. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer