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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: HHH maps its input to the behavior specified by it --- never reaches its halt state ---
Date: Fri, 16 Aug 2024 13:48:14 +0300
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On 2024-08-15 15:19:59 +0000, olcott said:

> On 8/15/2024 3:52 AM, Mikko wrote:
>> On 2024-08-14 13:47:16 +0000, olcott said:
>> 
>>> 
>>> _DDD()
>>> [00002172] 55         push ebp      ; housekeeping
>>> [00002173] 8bec       mov ebp,esp   ; housekeeping
>>> [00002175] 6872210000 push 00002172 ; push DDD
>>> [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
>>> [0000217f] 83c404     add esp,+04
>>> [00002182] 5d         pop ebp
>>> [00002183] c3         ret
>>> Size in bytes:(0018) [00002183]
>>> 
>>> The impossibility of DDD emulated by HHH
>>> (according to the semantics of the x86 language)
>>> to reach its own machine address [00002183] is
>>> compete proof.
>> 
>> No, it is not. Nothing is a proof except a proof.
> 
> An inductive proof of the execution trace shows that
> DDD emulated according to the semantics of the x86
> language cannot possibly reach machine address 00002183.

Note that induction is not a generally valid proof method.
Induction over natural numbers is valid because there is,
depending on the formalism, an induction axiom or axiom
scheme. There are other similar methods for other theories,
e.g. for set theory, but they are hardly relevant to
computation theory.

Some part of your claims may be provable with induction over natural
numbers but you have never presented any inductive proof.

-- 
Mikko