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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 21:51:29 -0500
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On 5/5/2025 9:27 PM, dbush wrote:
> On 5/5/2025 10:18 PM, olcott wrote:
>> On 5/5/2025 8:59 PM, dbush wrote:
>>> On 5/5/2025 8:57 PM, olcott wrote:
>>>> On 5/5/2025 7:49 PM, dbush wrote:
>>>>>
>>>>> Which starts with the assumption that an algorithm exists that 
>>>>> performs the following mapping:
>>>>>
>>>>>
>>>>> 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
>>>>>
>>>>>
>>>>>
>>>>>> DO COMPUTE THAT THE INPUT IS NON-HALTING
>>>>>> IFF (if and only if) the mapping FROM INPUTS
>>>>>> IS COMPUTED.
>>>>>
>>>>> i.e. it is found to map something other than the above function 
>>>>> which is a contradiction.
>>>>>
>>>>
>>>> The above function VIOLATES COMPUTER SCIENCE.
>>>> You make no attempt to show how my claim
>>>> THAT IT VIOLATES COMPUTER SCIENCE IS INCORRECT
>>>> you simply take that same quote from a computer
>>>> science textbook as the infallible word-of-God.
>>>
>>> All you are doing is showing that you don't understand proof by 
>>> contradiction, 
>>
>> Not at all. 
> 
> 
> Yes.
> 
> The mapping is well defined.  

You don't even know that "well defined" means
that all of the steps have been specified.

In mathematics, a well-defined expression or unambiguous
expression is an expression whose definition assigns it
a unique interpretation or value.
https://en.wikipedia.org/wiki/Well-defined_expression

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer