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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Mon, 24 Mar 2025 21:28:28 -0400
Organization: i2pn2 (i2pn.org)
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On 3/24/25 12:44 PM, olcott wrote:
> On 3/24/2025 10:14 AM, dbush wrote:
>> On 3/24/2025 11:03 AM, olcott wrote:
>>> On 3/24/2025 6:23 AM, Richard Damon wrote:
>>>> On 3/23/25 11:09 PM, olcott wrote:
>>>>> It is impossible for HHH compute the function from the direct
>>>>> execution of DDD because DDD is not the finite string input
>>>>> basis from which all computations must begin.
>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>
>>>> WHy isn't DDD made into the correct finite string?i
>>>>
>>>
>>> DDD is a semantically and syntactically correct finite
>>> stirng of the x86 machine language.
>>
>> Which includes the machine code of DDD, the machine code of HHH, and 
>> the machine code of everything it calls down to the OS level.
>>
>>>
>>>> That seems to be your own fault.
>>>>
>>>> The problem has always been that you want to use the wrong string 
>>>> for DDD by excluding the code for HHH from it.
>>>>
>>>
>>> DDD emulated by HHH directly causes recursive emulation
>>> because it calls HHH(DDD) to emulate itself again. HHH
>>> complies until HHH determines that this cycle cannot
>>> possibly reach the final halt state of DDD.
>>>
>>
>> Which is another way of saying that HHH can't determine that DDD halts 
>> when executed directly.
>>
> 
> given an input of the function domain it can
> return the corresponding output.
> https://en.wikipedia.org/wiki/Computable_function
> 
> Computable functions are only allowed to compute the
> mapping from their input finite strings to an output.
> 

Nope, got the requirement a bit sideways. The only CAN compute the 
mapping there code generates as the output, but MUST compute the mapping 
they are defined to compute to be correct.

Thus, since the Halting Mapping is from the description of the Program, 
to whether that program itself when run will halt, if that mapping was 
computable, there would exist a program that could do it. Since there 
isn't one, as proven by Turing, the Halting Mapping isn't a Computable 
Function.

Your flaw is that you PRESUME computability just because you are writing 
a program, and fail to understand that not all functions are, in fact, 
computable

You run into this confusion because you just failed to learn the meaning 
of the basic terms of the field, and just made up your own, so you 
became just an ignorant lying fraudster.