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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Fri, 2 May 2025 09:32:50 -0400
Organization: i2pn2 (i2pn.org)
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On 5/1/25 9:55 PM, olcott wrote:
> On 5/1/2025 8:42 PM, dbush wrote:
>> On 5/1/2025 9:26 PM, olcott wrote:
>>> On 5/1/2025 8:14 PM, dbush wrote:
>>>> On 5/1/2025 9:09 PM, olcott wrote:
>>>>> On 5/1/2025 7:32 PM, André G. Isaak wrote:
>>>>>> On 2025-05-01 14:15, olcott wrote:
>>>>>>> On 5/1/2025 10:14 AM, André G. Isaak wrote:
>>>>>>>> On 2025-04-30 21:50, olcott wrote:
>>>>>>>>> On 4/30/2025 7:17 PM, André G. Isaak wrote:
>>>>>>>>
>>>>>>>>>> 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; }
>>>>>>>>
>>>>>>>> All you're demonstrating here is that you have no clue what a 
>>>>>>>> function is, nor, apparently, do you have any desire to learn.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> What I am explaining is that a halt decider
>>>>>>> must compute the mapping FROM THE INPUTS ONLY
>>>>>>> by applying a specific set of finite string
>>>>>>> transformations to the inputs.
>>>>>>
>>>>>> No. Halt deciders weren't even mentioned above. I was addressing 
>>>>>> your absurd claim that int foo(int x, int y) { return 5; } does 
>>>>>> not compute a function. This clearly indicates that you do not 
>>>>>> grasp the concept of "function".
>>>>>>
>>>>>
>>>>> This is a brand new elaboration of computer
>>>>> science that I just came up with.
>>>>>
>>>>> It is common knowledge THAT inputs must correspond
>>>>> to OUTPUTS. What is totally unknown and brand new
>>>>> created by me is HOW inputs are made to correspond
>>>>> to OUTPUTS.
>>>>>
>>>>> Specific finite string transformation rules are
>>>>> applied to inputs to derive outputs.
>>>>
>>>> In other words, you're simply looking at an algorithm to see what 
>>>> mapping it computes
>>>>
>>>>>
>>>>> What everyone else has been doing is simply GUESSING
>>>>> that they correspond or relying on some authority
>>>>> that say they must correspond. (Appeal to authority error).
>>>>>
>>>>
>>>> False.  The halting problem proofs start with the assumption that 
>>>> the following requirements can be met and that HHH meets them:
>>>>
>>>>
>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>> instructions) X described as <X> with input Y:
>>>>
>>>> A solution to the halting problem is an algorithm H that computes 
>>>> the following mapping:
>>>>
>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>>>> directly
>>>>
>>>>
>>>
>>> For all of these years no one ever noticed that
>>> those requirements are incoherent 
>>
>> False.  The mapping exists and is well-defined, it's just that no 
>> algorithm can compute it, as Linz proved and you *explicitly* agreed.
>>
> 
> Specify every single step of the mapping and you will
> see that it has never been well defined. It has ONLY
> ever been a leap to a conclusion.

The mapping is infinite in size, so can't be fully written out.

Mappings don't HAVE "Steps", so you are showing your stupidity.

Now, if you claim that the results of running a program and seeing what 
it does have never been defined, then I guess you need to return all the 
pay you got for claiming to write programs that said they acheived 
specified requirements.

Now, in the field of Olcott Programming, where programs don't need to 
contain all their code, maybe the claim is true, but that isn't what 
people talk about when they talk about programs, and it your own invention.

All you are doing is proving your utter ignorance of what you talk about.