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From: Richard Damon <richard@damon-family.org>
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)
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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.