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

On Thursday, 2 December 2021 at 12:07:13 UTC+8, olcott wrote:
> ...
> Halting problem undecidability and infinitely nested simulation V2
>
> https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2
>

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

POH returns 1 or never returns. Do you agree?

On 12/1/21 11:07 PM, 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.
>
> 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
>
>
>

False, A given H will ALWAYS behave the same way, so the phrase, "for
any number o N steps", is meaningless. A given H will only and always
behave a given way. To argue of different Ns, you need a SET of Halt
Deciders, not A Halt decider. And you don't built the H^/P from 'a set'
of Halt deciders, but from a specific one.

The fix is to name each variation so every unique algorithm has a
distinct name.

IF we define Hn to be your simulating halt decider that will take N
steps to decide, then yes

If for all n, Hn(X,Y) will never reach a final state, the X(Y) is none
Halting. (but X and Y can't depend on n)

If we define Pm to use Hm and act contrary, then YES, if

Hn(Pm,Pm) would never halt for ALL values of n, then Pm(Pm) is none
halting and Hm(Pm,Pm) would be correct in saying non-halting, but for
every finite m there does exist an n enough greater than m where
Hn(Pm,Pm) will see the final state, thus we show that Pm(Pm) for all
finite m is halting.

You just don't understand how to handle actual logic.

FAIL.

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

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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 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.

>> 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.

1 is an arbitrary element of the set of positive integers. So according
to you if a computation doesn't reach its final state after one step it
is non-halting.

André

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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.

>>> 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.
> > 1 is an arbitrary element of the set of positive integers. So according
> to you if a computation doesn't reach its final state after one step it
> is non-halting.
>
> André
>

--
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 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?

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'.
What if your decider aborts the input after X steps and the input halts
after X+1 steps?

André

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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.

> 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).

> What if your decider aborts the input after X steps and the input halts
> after X+1 steps?
>
> André
>

It can be analytically determined on the basis of the infinite behavior
pattern of the input to H(P,P) that P never halts (dumb bunny).

--
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 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.

>> What if your decider aborts the input after X steps and the input
>> halts after X+1 steps?
>>
>> André
>>
>
> It can be analytically determined on the basis of the infinite behavior
> pattern of the input to H(P,P) that P never halts (dumb bunny).
But you've never offered any proof that your pattern is valid.

André

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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);
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).
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.

>>> What if your decider aborts the input after X steps and the input
>>> halts after X+1 steps?
>>>
>>> André
>>>
>>
>> It can be analytically determined on the basis of the infinite
>> behavior pattern of the input to H(P,P) that P never halts (dumb bunny).
> But you've never offered any proof that your pattern is valid.
>
> André
>

--
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 12/2/21 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);
> 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).
> 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.

But since H needs to be a SPECIFIC decider, which Simulate_Steps N value
does it use?

Once you chose that, then we can find a Simulate_Steps with ITS N high
enough for it to find the halting state.

FAIL.

Remember P is a SPECIFIC computation built with a SPECIFIC H which must
have a DEFINITE definition, thus it must be like just ONE of your
Simulate Steps calls.

This is maybe getting a bit better, maybe this is a Sophomore error.

>
>>>> What if your decider aborts the input after X steps and the input
>>>> halts after X+1 steps?
>>>>
>>>> André
>>>>
>>>
>>> It can be analytically determined on the basis of the infinite
>>> behavior pattern of the input to H(P,P) that P never halts (dumb bunny).
>> But you've never offered any proof that your pattern is valid.
>>
>> André
>>
>
>

On 2021-12-02 15:57, olcott wrote:

> 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.

So basically you have no idea what mathematical induction is.

André

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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.

>>>> What if your decider aborts the input after X steps and the input
>>>> halts after X+1 steps?
>>>>
>>>> André
>>>>
>>>
>>> It can be analytically determined on the basis of the infinite
>>> behavior pattern of the input to H(P,P) that P never halts (dumb bunny).
>> But you've never offered any proof that your pattern is valid.
>>
>> André
>>
>
>

On 12/2/2021 5:42 PM, André G. Isaak wrote:
> On 2021-12-02 15:57, olcott wrote:
>
>> 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.
>
> So basically you have no idea what mathematical induction is.
>
> André

Like a loop invariant continues to be true for every iteration of a loop
an invocation invariant remains true for every step of an invocation.

--
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 2021-12-02 17:16, olcott wrote:
> On 12/2/2021 5:42 PM, André G. Isaak wrote:
>> On 2021-12-02 15:57, olcott wrote:
>>
>>> 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.
>>
>> So basically you have no idea what mathematical induction is.
>>
>> André
>
> Like a loop invariant continues to be true for every iteration of a loop
> an invocation invariant remains true for every step of an invocation.

Which has exactly nothing to do with mathematical induction. You seem to
be responding with random remarks unrelated to what is written.

Mathematical induction requires that you demonstrate something along the
following lines as one of the steps in the induction:

For all X, if X has property P then X+1 has property P.

Where does such a demonstration appear in your 'induction' above?

André

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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.

On 12/2/2021 6:29 PM, André G. Isaak wrote:
> On 2021-12-02 17:16, olcott wrote:
>> On 12/2/2021 5:42 PM, André G. Isaak wrote:
>>> On 2021-12-02 15:57, olcott wrote:
>>>
>>>> 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.
>>>
>>> So basically you have no idea what mathematical induction is.
>>>
>>> André
>>
>> Like a loop invariant continues to be true for every iteration of a
>> loop an invocation invariant remains true for every step of an
>> invocation.
>
> Which has exactly nothing to do with mathematical induction. You seem to
> be responding with random remarks unrelated to what is written.
>
> Mathematical induction requires that you demonstrate something along the
> following lines as one of the steps in the induction:
>
> For all X, if X has property P then X+1 has property P.
>

X = sequential step of the simulation of the input to H(P,P)
property P = P(P) has not reached its final state at step X

For all X if P then for X+1 P

> Where does such a demonstration appear in your 'induction' above?
>
> André
>

--
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

On 12/2/21 8:17 PM, olcott wrote:
> On 12/2/2021 6:29 PM, André G. Isaak wrote:
>> On 2021-12-02 17:16, olcott wrote:
>>> On 12/2/2021 5:42 PM, André G. Isaak wrote:
>>>> On 2021-12-02 15:57, olcott wrote:
>>>>
>>>>> 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.
>>>>
>>>> So basically you have no idea what mathematical induction is.
>>>>
>>>> André
>>>
>>> Like a loop invariant continues to be true for every iteration of a
>>> loop an invocation invariant remains true for every step of an
>>> invocation.
>>
>> Which has exactly nothing to do with mathematical induction. You seem
>> to be responding with random remarks unrelated to what is written.
>>
>> Mathematical induction requires that you demonstrate something along
>> the following lines as one of the steps in the induction:
>>
>> For all X, if X has property P then X+1 has property P.
>>
>
> X = sequential step of the simulation of the input to H(P,P)
> property P = P(P) has not reached its final state at step X
>
> For all X if P then for X+1 P
>

Lots of garbage.

Since H is a FIXED decider, and H WILL abort H()P,P) in some number n
steps, you don't have any 'proof' that a n+k step simulation of P(P)
will not halt.

In fact, we DO know that the simulation of P(P) WILL halt in some
fininte number of steps (as long as H(P,P) does return 0) as the direct
running of P(P), as you even admit, halts.

All your induction proof has shown is that NO version of your H can ever
see the halting of the P built on it, which does NOT prove the
non-halting for ANY version of your H.

FAIL.

>
>> Where does such a demonstration appear in your 'induction' above?
>>
>> André
>>
>
>

On 12/2/21 8:14 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.

I call him a liar be cause he uses that term on others.

It has been pointed out to him MANY times that he is wrong, and either
he is so mentally deficient that he is incapable of reason, or he is
chosing to be intentionally ignorant of the facts, which is in my books,
still lying.

On 12/2/21 8:57 PM, olcott wrote:
> 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.

LIE. You mis use the terms.

Since the direct running of P(P) DOES HALT, it does not halt because
ITSELF was aborted by

>
> 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.
>

THE LOOP YOU COMPLAIN ABOUT IS LEGAL.

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

Then H(P,P) never answer, and thus fails to be a decider.

IF you claim differently, then you have LIED about the qualities of H.

One requirement of H is that it must be a COMPUTATION, which means that
ALL COPIES of it behave the same given the same input. Remember, a
computation is an algorithm that computes a Mathematical function.

The mathematical property Halts(P,P) must have a value, it will either
be that P(P) Halts or P(P) never halts (and by definition will match
what that P(P) acutally does). H(P,P) to be a correct halting decider
means that ALL copies of H, given the input P,P, must give the value
that Halts(P,P) return, the ALL Copies of H must give the same answer,
and in finite time, and it needs to match the halting property of P(P).

On 12/2/21 4:44 PM, 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.

Except that for the case of P, we know that it WILL Halt. Given that
H)P,P) will halt after k steps and return 0, then the simulation of this
input, the computation P(P) for some number N that will be bigger than
k, we will reach the halting state.

It will take H some m steps to simulate k steps of P, and then it will
return 0, so in just a few steps more that the k steps to get to the
call to H, + m steps for that H to simulate its input, then a few to
return after that H returns 0, and the outer P will Halt.

Thus for N = k + m + some small number steps of simulation will see P(P)
halt.

FAIL.

Since N > k (by at least m) no H will get there, but it isn't H's
simulation that matters, it is the 'pure' simulation of the input that does.

>
>>>> 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.
>>  > 1 is an arbitrary element of the set of positive integers. So
>> according
>> to you if a computation doesn't reach its final state after one step
>> it is non-halting.
>>
>> André
>>
>
>

On 12/2/21 5:15 PM, 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.

No, you just misuse the term, and try to obfuscate things.

>
>> 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).

But you DO prove that if prop(n) is true, we can derive that prop(n+1)
is true, and that prop(0) (or sometimes prop(1) is true).

You haven't actually PROVED anything at all, just made claims.

>
>> What if your decider aborts the input after X steps and the input
>> halts after X+1 steps?
>>
>> André
>>
>
> It can be analytically determined on the basis of the infinite behavior
> pattern of the input to H(P,P) that P never halts (dumb bunny).
>
No, you haven't, because you use a wrong pattern. It only proves that P
is non-halting fof the case where H unconditionally executes/simulates
its input, but in that case, H never returns an answer, so that H still
fails (but 0 would have been the right answer).

On 03/12/2021 02:36, Richard Damon wrote:
> On 12/2/21 8:14 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.
>
>
> I call him a liar be cause he uses that term on others.

Fair point, but I'd say PO has the "excuse" of literally not
understanding that everyone else is far more competent than him, due to
his problems. Probably his view is that his arguments are genuine
"logical reasoning", and I doubt he even understands what the difference
is between his arguments and those of other responders. I don't think
he understands what a proof needs to be, or really why one is needed -
when he is presented with a proof, he has no way of following it in the
way other people do, so it just seems to be someone making claims to try
to win their side of an argument. So when someone else doesn't agree
with his claims he is genuinely confused as to why that should be -
either people are /deliberately/ biassed against him, or they're just
too stupid (or lack the expertise etc.) to follow his "reasoning".

ok, that's exactly your position in the next paragraph :)

>
> It has been pointed out to him MANY times that he is wrong, and either
> he is so mentally deficient that he is incapable of reason,

Yes, I think he is indeed incapable of (all higher forms of) reasoning.