If for any number of N steps that simulating halt decider H simulates
its input (X,Y) X never reaches its final state then we know that X
never halts and H is always correct to abort the simulation of this
input and return 0.

This is the invocation invariant of the input similar to the loop
invariant and recursion invariant of proof of program correctness.

https://en.wikipedia.org/wiki/Invariant_(mathematics)

Halting problem undecidability and infinitely nested simulation V2

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

Olcott failed Logic, but is trying to help lobsters and crabs. Let us give a hand clap to the spammer for trying to reform, his punk and mindless life in academics for he can never understand he is a academic failure.
>
>
>
> ////////
> |:---[.]
> |( _J
> | ^ ( _|
> / \_____)
> / _____ \
> | / \ .
> | | |
> \ /\ /\__
> | | \/---
> \ \ )________________\\ \\\
> | >_____/_____)============
> \__________/ ==============
> / \ -----------------------------// ///
> | | ~~
> \ \\
> \ |\
> \ | \
> \ | |
> | | |
> | | |
> | / |
> |________/____|
> (_________)____)
>

Olcott can David Sainsbury, Peter Johnstone, Imre Leader, Gabriel Paternain ever do a geometry proof of Fundamental Theorem of Calculus, or is that totally foreign to them? Mind you, not a limit analysis hornswaggle for that is not geometry, limit analysis is not even a math proof for anyone can analysis things, analysis this post and only math hypocrites would think it is a proof.

Olcott can Heine, Hine, Hobson, Hope-Coles, Howie, ever ask the question, which is the atom's real electron, the muon stuck inside a 840MeV proton torus doing the Faraday law or the 0.5MeV particle that AP calls the Dirac magnetic monopole. Or does that thought fly way too above their heads?



Olcott, why cannot Haniff, Heavens-Ward, Heine, Hine, Hobson, Hope-Coles, Howie, Hughes, Irvine, Jardine ask the question which is the atom's real electron-- muon or 0.5MeV particle? Is it because they cannot even do logic correctly with their 2 OR 1 = 3 with AND as subtraction?
>
> Olcott why does Cambridge Univ Stephen J. Toope, David Sainsbury, Peter Johnstone, Imre Leader, Gabriel Paternain keep teaching Boole error filled logic of 2 OR 1 = 3 with AND as subtraction, and never a geometry proof of Fundamental Theorem of Calculus and these crazies still think the slant cut in cone is a ellipse when in fact it is a Oval. Why brainwash and pollute more students like Pete Olcott who is crazy enough as it is.
>
> Olcott why is noone in Cambridge physics able to ask the question which is the atom's true real electron-- muon or 0.5MeV particle? Sargent, Saunders, Saxena, Schneider, Scott, Scrivener, Sebastian, Simmons, Simons, Sirringhaus, Smith?? Do they not have a brain to ask a simple question????
>
> 3rd published book
>
> AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
> by Archimedes Plutonium (Author)
>
> Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.
>
> Length: 21 pages
>
> File Size: 1620 KB
> Print Length: 21 pages
> Publication Date: March 11, 2019
> Sold by: Amazon Digital Services LLC
> Language: English
> ASIN: B07PLSDQWC
> Text-to-Speech: Enabled
> X-Ray: Not Enabled
> Word Wise: Not Enabled
> Lending: Enabled
> Enhanced Typesetting: Enabled
>
>
> #8-2, 11th published book
>
> World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
> by Archimedes Plutonium (Author)
>
> Last revision was 19May2021. This is AP's 11th published book of science.
> Preface:
> Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
>
> Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis".. To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?
>
> Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.
>
> Length: 137 pages
>
> Product details
> ASIN : B07PQTNHMY
> Publication date : March 14, 2019
> Language : English
> File size : 1307 KB
> Text-to-Speech : Enabled
> Screen Reader : Supported
> Enhanced typesetting : Enabled
> X-Ray : Not Enabled
> Word Wise : Not Enabled
> Print length : 137 pages
> Lending : Enabled
> Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> #2 in 45-Minute Science & Math Short Reads
> #134 in Calculus (Books)
> #20 in Calculus (Kindle Store)
>
> 5th published book
>
> Suspend all College Classes in Logic, until they Fix their Errors // Teaching True Logic series, book 1 Kindle Edition
> by Archimedes Plutonium (Author)
>
> Last revision was 29Mar2021. This is AP's 5th published book of science.
> Preface:
> First comes Logic-- think straight and clear which many logic and math professors are deaf dumb and blind to, and simply refuse to recognize and fix their errors.
>
> The single biggest error of Old Logic of Boole and Jevons was their "AND" and "OR" connectors. They got them mixed up and turned around. For their logic ends up being that of 3 OR 2 = 5 with 3 AND 2 = either 3 or 2 but never 5, when even the local village idiot knows that 3 AND 2 = 5 (addition) with 3 OR 2 = either 3 or 2 (subtraction). The AND connector in Logic stems from the idea, the mechanism involved, that given a series of statements, if just one of those many statements has a true truth value, then the entire string of statements is overall true, and thus AND truth table is truly TTTF and never TFFF. And secondly, their error of the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability end conclusion.
>
> My corrections of Old Logic have a history that dates before 1993, sometime around 1991, I realized the Euclid proof of infinitude of primes was illogical, sadly sadly wrong, in that the newly formed number by "multiply the lot and add 1" was necessarily a new prime in the indirect proof method. So that my history of fixing Old Logic starts in 1991, but comes to a synthesis of correcting all four of the connectors of Equal/not, And, Or, If->Then, by 2015.
>
> Cover picture: some may complain my covers are less in quality, but I have a good reason for those covers-- I would like covers of math or logic to show the teacher's own handwriting as if he were back in the classroom writing on the blackboard or an overhead projector.
>
>
> Length: 72 pages
>
> File Size: 773 KB
> Print Length: 72 pages
> Publication Date: March 12, 2019
> Sold by: Amazon Digital Services LLC
> Language: English
> ASIN: B07PMB69F5
> Text-to-Speech: Enabled
> X-Ray: 
Not Enabled 

> Word Wise: Not Enabled
> Lending: Enabled
> Screen Reader: Supported
> Enhanced Typesetting: Enabled
> 

>
>
> #6-2, 27th published book
>
> Correcting Reductio Ad Absurdum// Teaching True Logic series, book 2 Kindle Edition
> by Archimedes Plutonium (Author)
>
>
> Last revision was 9NOV2020. This is AP's 27th published book.
>
> Preface:
> These are the TRUE Truth Tables of the 4 connectors of Logic
>
> Equal+Not
> T = T = T
> T = ~F = T
> F = ~T = T
> F = F = T
>
> If--> then
> T --> T = T
> T --> F = F
> F --> T = U (unknown or uncertain)
> F --> F = U (unknown or uncertain)
>
> And
> T & T = T
> T & F = T
> F & T = T
> F & F = F
>
>
> Or
> T or T = F
> T or F = T
> F or T = T
> F or F = F
>
> Those can be analyzed as being Equal+Not is multiplication. If-->then is division. And is addition and Or is subtraction in mathematics. Now I need to emphasis this error of Old Logic, the If->Then conditional. I need to make it clear enough to the reader why the true Truth Table of IF --> Then requires a U for unknown or uncertain with a probability outcome for F --> T = U and F --> F = U. Some smart readers would know that the reason for the U is because without the U, Logic has no means of division by 0 which is undefined in mathematics. You cannot have a Logic that is less than mathematics. A logic that is impoverished and cannot do a "undefined for division by 0 in mathematics". The true logic must be able to have the fact that division by 0 is undefined. True logic is larger than all of mathematics, and must be able to fetch any piece of mathematics from out of Logic itself. So another word for U is undefined. And this is the crux of why Reductio ad Absurdum cannot be a proof method of mathematics, for a starting falsehood in a mathematics proof can only lead to a probability unknown, undefined end conclusion.
>
> Now in Old Logic they had for Reductio Ad Absurdum as displayed by this schematic:
>
> | | ~p
> | |---
> | | .
> | | .
> | | q
> | | .
> | | .
> | | ~q
> | p
>
> Which is fine except for the error of not indicating the end conclusion of "p" is only a probability of being true, not guaranteed as true. And this is the huge huge error that mathematicians have fallen victim of. For the Reductio Ad Absurdum is not a proof method for mathematics, it is probability of being true or false. Math works on guaranteed truth, not probability. This textbook is written to fix that error.
> Length: 86 pages
>
> Product details
> • ASIN : B07Q18GQ7S
> • Publication date : March 23, 2019
> • Language : English
> • File size : 1178 KB
> • Text-to-Speech : Enabled
> • Enhanced typesetting : Enabled
> • X-Ray : Not Enabled
> • Word Wise : Not Enabled
> • Print length : 86 pages
> • Lending : Enabled
> • Best Sellers Rank: #346,875 in Kindle Store (See Top 100 in Kindle Store)
> ◦ #28 in Logic (Kindle Store)
> ◦ #95 in Two-Hour Science & Math Short Reads
> ◦ #217 in Mathematical Logic
> •
>
>

On 2021-12-01 21:07, olcott wrote:
> If for any number of N steps that simulating halt decider H simulates
> its input (X,Y) X never reaches its final state then we know that X
> never halts and H is always correct to abort the simulation of this
> input and return 0.

What on earth is N? If that is simply a variable which can be anything
then you seem to be saying that if for 1 step the simulated input
doesn't halt then it never halts. This means pretty much every
computation whose initial state is not also a final halting state
doesn't halt according to you.

> This is the invocation invariant of the input similar to the loop
> invariant and recursion invariant of proof of program correctness.

That sentence could probably use some vinaigrette. Or syrup of ipecac.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

On 12/2/2021 12:09 PM, André G. Isaak wrote:
> On 2021-12-01 21:07, olcott wrote:
>> If for any number of N steps that simulating halt decider H simulates
>> its input (X,Y) X never reaches its final state then we know that X
>> never halts and H is always correct to abort the simulation of this
>> input and return 0.
>
> What on earth is N?

any arbitrary element of the set of positive integers

> If that is simply a variable which can be anything
> then you seem to be saying that if for 1 step the simulated input
> doesn't halt then it never halts. This means pretty much every
> computation whose initial state is not also a final halting state
> doesn't halt according to you.
>
>> This is the invocation invariant of the input similar to the loop
>> invariant and recursion invariant of proof of program correctness.
>
> That sentence could probably use some vinaigrette. Or syrup of ipecac.
>
> André
>

Invariants are the key element of mathematical proof of program
correctness. https://en.wikipedia.org/wiki/Invariant_(mathematics)

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

On 12/2/2021 7:14 PM, Mike Terry wrote:
> On 02/12/2021 23:54, Richard Damon wrote:
>> On 12/2/21 5:57 PM, olcott wrote:
>>> On 12/2/2021 4:45 PM, André G. Isaak wrote:
>>>> On 2021-12-02 15:15, olcott wrote:
>>>>> On 12/2/2021 3:52 PM, André G. Isaak wrote:
>>>>>> On 2021-12-02 14:44, olcott wrote:
>>>>>>> On 12/2/2021 3:25 PM, André G. Isaak wrote:
>>>>>>>> On 2021-12-02 13:29, olcott wrote:
>>>>>>>>> On 12/2/2021 12:09 PM, André G. Isaak wrote:
>>>>>>>>>> On 2021-12-01 21:07, olcott wrote:
>>>>>>>>>>> If for any number of N steps that simulating halt decider H
>>>>>>>>>>> simulates its input (X,Y) X never reaches its final state
>>>>>>>>>>> then we know that X never halts and H is always correct to
>>>>>>>>>>> abort the simulation of this input and return 0.
>>>>>>>>>>
>>>>>>>>>> What on earth is N?
>>>>>>>>>
>>>>>>>>> any arbitrary element of the set of positive integers
>>>>>>>>
>>>>>>>> And right below I explain why this leads to a nonsensical
>>>>>>>> interpretation. Of course, you ignored this.
>>>>>>>>
>>>>>>>
>>>>>>> Because there exists no N in the set of positive integers such
>>>>>>> that N steps of the simulation of the input H(X,Y) stops running
>>>>>>> we correctly conclude that (this invocation invariant proves) the
>>>>>>> input to H(X,Y) never stops running.
>>>>>>
>>>>>> So you mean 'every N' rather than 'any N'. But this just amounts
>>>>>> to saying that if X doesn't halt that it is non-halting, so why
>>>>>> bring up N at all?
>>>>>>
>>>>>
>>>>> Because my reviewers seem too dense to comprehend it any other way.
>>>>
>>>> Your "reviewers" can't understand 'every' and insist you use 'any'?
>>>>
>>>>>> But your decider, if it decides to abort its input, must do so
>>>>>> after some FINITE number of steps, so it cannot actually test for
>>>>>> 'every N'.
>>>>>
>>>>> Do you test every N in mathematical induction? (Of course not you
>>>>> dumb bunny).
>>>>
>>>> Nowhere does your 'proof' make use of anything even remotely
>>>> analogous to mathematical induction.
>>>>
>>>
>>> First, the relevant property P(n) is proven for the base case, which
>>> often corresponds to n = 0 or n = 1. Then we assume that P(n) is
>>> true, and we prove P(n+1). The proof for the base case(s) and the
>>> proof that allows us to go from P(n) to P(n+1) provide a method to
>>> prove the property for any given m >= 0 by successively proving P(0),
>>> P(1), ..., P(m). We can't actually perform the infinity of proves
>>> necessary for all choices of m >= 0, but the recipe that we provided
>>> assures us that such a proof exists for all choices of m.
>>>
>>> To reduce the possibility of error, we will structure all our
>>> induction proofs rigidly, always highlighting the following four parts:
>>>
>>> The general statement of what we want to prove;
>>> The specification of the set we will perform induction on;
>>> The statement and proof of the base case(s);
>>
>> And where is the PROOF?
>>
>>> The statement of the induction hypothesis (generally, we will assume
>>> that P(n) holds, but sometimes we need stronger assumptions, see
>>> below), the statement of P(n+1) and proof of the induction step (or
>>> case).
>>
>> And where is the PROOF?
>>
>>> https://www.cs.cornell.edu/courses/cs312/2004fa/lectures/lecture9.htm
>>
>>
>>
>>>
>>> Simulate_Steps(P,P,0)   P(P) does not reach its final state.
>>> Simulate_Steps(P,P,N)   P(P) does not reach its final state.
>>> Simulate_Steps(P,P,N+1) P(P) does not reach its final state.
>>> ∴ the input to H(P,P) never halts.
>>>
>>
>> These are just STATEMENTS, you haven't PROVED anything.
>>
>> I guess that just shows mow much you LIE.
>
> You call PO a liar quite a lot, but to be a liar PO would need to be
> deliberately trying to deceive you.  Do you think that's the case?  Or
> is it reasonable to think that PO /believes/ what he said above is a
> genuine application of the mathematical principle of induction.  [Yes,
> PO has no logical /grounds/ for thinking that, since he lacks any
> understanding of the principle, but the question is about what PO
> /believes/.]
>
> Personally, I would say PO genuinely doesn't understand that his
> arguments are idiotic, due to some psychological/neural problem.  I see
> his claims and reasoning he puts forward for them more akin to
> confabulation, where a patient invents memories and explanations for a
> state of affairs they believe to be true, without necessarily having any
> deceptive intent.
>
> Of course, there are cases where PO repeats claims (like where he
> repeats his obviously false claim to have had fully coded TMs a couple
> of years ago), even AFTER it is explained that what he is saying does
> not correspond to accepted wording of the terms used, and so is simply
> false.  Maybe it's hard to swallow that this might not be direct lying
> on PO's part, but even in these situations I suspect his
> mind/memory/understanding is so "malleable" that /to him/ it really does
> seem that he was telling the truth all the time??
>
> I don't really /know/ whether PO is conciously lying in these cases, but
> it does seem to me that PO is so thoroughly DELUDED that he could look
> at someone holding up 4 fingers and convince himself that, yes there are
> 4 fingers, but also it is correct that there are 5, or 3, for some
> reason!  (And genuinely believe that - not just be lying about it...) He
> is perhaps the ideal citizen of Oceana!  :)  Or, perhaps in his heart he
> knows he is making false claims - not easy to say either way.
>
> Perhaps a bigger point is that it doesn't really matter either way
> whether PO is actually lying or confabulating or some third option - I'm
> not even sure the distinction is meaningful in PO's case.  What he says
> is all totally irrelevant, and even if someone "proved" the PO was
> "lying" it would make no difference whatsoever to anything...
>
>
> Mike.

It is true that when-so-ever any input to simulating halt decider H(X,Y)
only stops running when its simulation has been aborted that this input
is correctly decided as not halting.

This does eliminate the conventional halting problem feedback loop
between the halt decider and its input that would otherwise make this
input undecidable to this decider.

int main() { P(P); } calls H(P,P) simulates P(P) that never halts.

Halting problem undecidability and infinitely nested simulation V2
https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer