#include <stdint.h>
#include <stdio.h>
typedef int (*ptr)();

int H(ptr x, ptr y)
{ x(y); // direct execution of P(P)
return 1;
}

// Minimal essence of Linz(1990) Ĥ
// and Strachey(1965) P
int P(ptr x)
{ H(x, x);
return 1; // Give P a last instruction at the "c" level
}

int main(void)
{ H(P, P);
}

PSR set: It is self evident that when 0 to ∞ steps of the input to
H(P,P) are directly executed or correctly simulated that the input to
H(P,P) never reaches its final instruction.

We can think of the combinations of (H,P) as an enumerated sequence of
finite strings of C source-code. The above source code specifies the
H0(P0,P0) first element of this sequence.

Computation that halts
a computation is said to halt whenever it enters a final state.
(Linz:1990:234)

PSR subset A: When Hn(Pn, Pn) executes or simulates a fixed number of N
steps of its input this input still never reaches its last instruction
and Hn(Pn, Pn) halts.

PSR subset B: When Hn(Pn, Pn) executes or simulates a fixed number of N
steps of its input this input still never reaches its last instruction
and Hn(Pn, Pn) halts and Pn(Pn) called from main() halts.

PSR subset C: For the subset of PSR subset A where Hn(Pn, Pn) returns 0
the returned halt status corresponds to the actual behavior of the input
to Hn(Pn, Pn).

PSR subset D: For the subset of PSR subset C where Hn(Pn, Pn) returns 0
on the basis that this input matches the infinite recursion behavior
pattern. Hn(Pn, Pn) detects that its input is calling H again with the
same input that it was called with. This makes Hn a correct halt decider
of this input.

H is a computable function that accepts or rejects inputs in its domain
on the basis that these inputs specify a sequence of configurations that
reach their final state.

--
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 11/24/2021 2:56 PM, André G. Isaak wrote:
> On 2021-11-24 13:41, olcott wrote:
>> On 11/24/2021 1:48 PM, André G. Isaak wrote:
>>> On 2021-11-24 12:36, olcott wrote:
>>>> On 11/24/2021 1:19 PM, André G. Isaak wrote:
>
>>> But the halting *function* doesn't involve any decider. It is simply
>>> a mapping from computations to their halting status.
>>>
>>> Again, reread what I wrote. Mathematical functions don't involve
>>> "invoking" anything. They are simply mappings, i.e. sets of ordered
>>> pairs.
>>>
>>> The job of a halt *decider* is to compute the mappings contained in
>>> that function.
>>>
>>
>> a decider always maps finite strings to accept reject states.
>
> Yes, it maps finite strings to accepting or rejecting states, but in
> doing so it computes a *function*. I am asking you to think about what
> that function is, not about the decider itself. The function is prior to
> the decider.
>
> Please explain how the ordered pair ((P, P), true) involves any sort of
> reference, let alone 'pathological self reference'. That is the relevant
> element of the halting *function* which your decider allegedly computes.
>
>> You keep simply ignoring the fact the an input with pathological
>> self-reference has different behavior than one that does not.
>> You keep trytng to simply assume away verified facts.
>
> Again, I am trying to get you to focus on the halting *function*, not on
> your H. We can come back to your H once you demonstrate that you
> understand what the distinction between the halting function and a halt
> decider is, but you seem determined not to understand this.
>
>>>> The mapping to a digraph contains cycles that do not exist for other
>>>> inputs.
>>>>> Linz demonstrates that this isn't possible. *YOU'VE* demonstrated
>>>>> that this isn't possible but you keep trying to change the rules of
>>>>> the game so you can maintain that your 'decider' is somehow getting
>>>>> the right answer when it is not. A halt decider must compute the
>>>>> halting function as described above.
>>>>>
>>>>
>>>>
>>>> Computable functions are the basic objects of study in computability
>>>> theory. Computable functions are the formalized analogue of the
>>>> intuitive notion of algorithms,
>>>
>>> No, they are not. A computable function is a function for which it is
>>> *possible* to construct an algorithm. But a computable function is
>>> *not* an algorithm. It is simply a set of ordered pairs.
>>>
>>> Once again, I ask, why is it that when people attempt to correct you
>>> on your misuse of terminology you insist on doubling down rather than
>>> carefully reading what is said to try to understand the distinction
>>> between terms that is being brought to your attention?
>>>
>>> André
>>>
>>
>> You are correcting an encyclopedia.
>> deciders are a specific type of computable function that
>> maps finite strings to accept reject states.
>
> No. I am correcting you.
>
> Deciders are a specific type of turing machine which *computes* a
> computable function. Something which computes a function is not the same
> thing as that function.
>
> A function is a mapping.
>
> A computation is an alogorithm.
>
> A computable function is a function for which an algorithm exists for
> computing that function.
>
> A decider is related to some computable function. That doesn't make it a
> computable function.
>
> André
>

The sequence of 1 to N configurations specified by the input to H(X, Y)
cannot be correctly construed as anything other than the sequence of 1
to N steps of the (direct execution, x86 emulation or UTM simulation of
this input).

--
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 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
> •
>
>
> True Chemistry: Chemistry Series, book 1 Kindle Edition
> by Archimedes Plutonium (Author)
>
> Physics and chemistry made a mistake in 1897 for they thought that J.J. Thomson's small particle of 0.5MeV was the electron of atoms. By 2017, Archimedes Plutonium discovered that the rest mass of 940 for neutron and proton was really 9 x 105MeV with a small sigma-error. Meaning that the real proton is 840MeV, real electron is 105 MeV= muon, and that little particle Thomson discovered was in fact the Dirac magnetic monopole. Dirac circa 1930s was looking for a magnetic monopole, and sadly, Dirac passed away before 2017, because if he had lived to 2017, he would have seen his long sought for magnetic monopole which is everywhere.
>
> Cover picture: shows 3 isomers of CO2 and the O2 molecule.
>
> Length: 1150 pages
>
>
> Product details
> • File Size : 2167 KB
> • ASIN : B07PLVMMSZ
> • Publication Date : March 11, 2019
> • Word Wise : Enabled
> • Print Length : 1150 pages
> • Language: : English
> • Text-to-Speech : Not enabled
> • Enhanced Typesetting : Enabled
> • X-Ray : Not Enabled
> • Lending : Enabled
> Amazon Best Sellers Rank: #590,212 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
> #181 in General Chemistry & Reference
> #1324 in General Chemistry
> #1656 in Physics (Kindle Store)
>
>
> Cambridge professors insane about Logic turns students like Pete Olcott insane also.
>
> Cambridge Physics Dept
>
> Ahnert, Alai, Alexander, Allison, Ansorge, Atature, Barker, Barnes, Bartlett, Batley, Baumberg, Bohndiek, Bowman, Brown, Buscher, Butler, Campbell Carilli, Carter, Castelnovo, Challis, Chalut, Chaudhri, Chin, Ciccarelli, Cicuta, Cole, Cooper, Cowburn, Credgington, Cross, Croze, Deschler, Donald, Duffett-Smith, Dutton, Eiser, Ellis, Euser, Field, Flynn, Ford, Friend, Gibson, Green, Greenham, Gripaios, Grosche, Guck, Gull, Haniff, Heavens-Ward, Heine, Hine, Hobson, Hope-Coles, Howie, Hughes, Irvine, Jardine, Jenkins, Jones, Josephson, Keyser, Khmeinitskii, King, Kotlyar, Lamacraft, Lasenby, Lester, Longair, Lonzarich, Maiolino, Marshall, Martin, Mitov, Morris, Mortimer, Moller, Needs, Norman, Nunnenkamp, Padman,Parker, Patel, Payne, Pepper, Phillips, Pramauro, Queloz, Rao, Richer, Riley, Ritchie, Sargent, Saunders, Saxena, Schneider, Scott, Scrivener, Sebastian, Simmons, Simons, Sirringhaus, Smith, Sutherland, Taylor, Teichmann, Terentjev, Thomson, Verrechia, Walker, Ward, Warner, Weale, Webber, Whyles, Withington.
>
> Cambridge Math Dept
>
> Alan Baker
> Bela Bollobas
> Darwin Smith
> John Coates
> Timothy Gowers
> Peter Johnstone
> Imre Leader
> Gabriel Paternain
>
> Can any-one at Cambridge start correcting the error filled Boole, Jevons, Russell, Whitehead, Godel, Wittgenstein, all failures of logic and logical reasoning, include Cantor and his tripe of undefined infinity, an infinity without a borderline between finite and infinite.
>
> Cambridge, you no longer are a premiere University but a school that fosters and shelters losers of logical reasoning.
>
> AP, King of Science, especially Physics
