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How can we decide a function is undecidable?

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  How can we decide a function is undecidable? wij <wyniijj@gmail.com> - 2021-08-30 09:20 -0700
    Re: How can we decide a function is undecidable? "dklei...@gmail.com" <dkleinecke@gmail.com> - 2021-08-30 10:00 -0700
      Re: How can we decide a function is undecidable? olcott <NoOne@NoWhere.com> - 2021-08-30 12:20 -0500
      Re: How can we decide a function is undecidable? wij <wyniijj@gmail.com> - 2021-08-31 02:26 -0700
        Re: How can we decide a function is undecidable? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-08-31 15:09 +0100
    Re: How can we decide a function is undecidable? olcott <NoOne@NoWhere.com> - 2021-08-31 08:44 -0500
      Re: How can we decide a function is undecidable? Richard Damon <Richard@Damon-Family.org> - 2021-08-31 18:52 -0400

#38550 — How can we decide a function is undecidable?

Let function mean a deterministic process, like the function of mathematics
https://en.wikipedia.org/wiki/Function_(mathematics)
X:X->Y
given a function f∈X taking input x∈X and output a deterministic y∈Y.
The point here is that X, entity of the function f can be anything,
including any super intelligent being who acts as a function, e.g. alien
creature, god,...,etc.

No function f can decide the property of another function g that g can defy.
GUR(v4) https://groups.google.com/g/comp.theory/c/_tbCYyMox9M

Thus, the conventional HP is a sub-instance of GUR.
This is a more general and much stronger statement than Gödel's incompleteness 
theorems (mathematical formal system) and Rice's theorem(algorithm), because
GUR states about ANY function entity.

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#38552

On Monday, August 30, 2021 at 9:20:18 AM UTC-7, wij wrote:
> Let function mean a deterministic process, like the function of mathematics 
> https://en.wikipedia.org/wiki/Function_(mathematics) 
> X:X->Y 

That is exactly wrong as the definition of a function in mathematics.

A mathematical function is usually defined as a set of ordered pairs.

Long ago - Ike Newton's days - functions were thought of as processes. 
Mathematicians have done better since 1800. 

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#38555

On 8/30/2021 12:00 PM, dklei...@gmail.com wrote:
> On Monday, August 30, 2021 at 9:20:18 AM UTC-7, wij wrote:
>> Let function mean a deterministic process, like the function of mathematics
>> https://en.wikipedia.org/wiki/Function_(mathematics)
>> X:X->Y
> 
> That is exactly wrong as the definition of a function in mathematics.
> 
> A mathematical function is usually defined as a set of ordered pairs.
> 

The linked definition seems to be merely a paraphrase.

In mathematics, a function[note 1] is a binary relation between two sets 
that associates each element of the first set to exactly one element of 
the second set. Typical examples are functions from integers to 
integers, or from the real numbers to real numbers.

> Long ago - Ike Newton's days - functions were thought of as processes.
> Mathematicians have done better since 1800.
> 


-- 
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre 
minds." Einstein

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#38589

On Tuesday, 31 August 2021 at 01:00:49 UTC+8, dklei...@gmail.com wrote:
> On Monday, August 30, 2021 at 9:20:18 AM UTC-7, wij wrote: 
> > Let function mean a deterministic process, like the function of mathematics 
> > https://en.wikipedia.org/wiki/Function_(mathematics) 
> > X:X->Y
> That is exactly wrong as the definition of a function in mathematics. 
> 
> A mathematical function is usually defined as a set of ordered pairs. 
 
"associating x to y" is a process. A hidden variable is 'time'.
'ordered pair' has no concept of time.

> Long ago - Ike Newton's days - functions were thought of as processes. 
> Mathematicians have done better since 1800.

Prove it.

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#38597

wij <wyniijj@gmail.com> writes:

> On Tuesday, 31 August 2021 at 01:00:49 UTC+8, dklei...@gmail.com wrote:

>> A mathematical function is usually defined as a set of ordered pairs. 
>  
> "associating x to y" is a process. A hidden variable is 'time'.
> 'ordered pair' has no concept of time.

Yes, that's why the "function as a process" is not the one that's used.
The notation f: X -> Y means f is a subset of X x Y with the key
"function" property (that images are unique).

-- 
Ben.

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#38594

On 8/30/2021 11:20 AM, wij wrote:
> Let function mean a deterministic process, like the function of mathematics
> https://en.wikipedia.org/wiki/Function_(mathematics)
> X:X->Y
> given a function f∈X taking input x∈X and output a deterministic y∈Y.
> The point here is that X, entity of the function f can be anything,
> including any super intelligent being who acts as a function, e.g. alien
> creature, god,...,etc.
> 
> No function f can decide the property of another function g that g can defy.
> GUR(v4) https://groups.google.com/g/comp.theory/c/_tbCYyMox9M
> 
> Thus, the conventional HP is a sub-instance of GUR.
> This is a more general and much stronger statement than Gödel's incompleteness
> theorems (mathematical formal system) and Rice's theorem(algorithm), because
> GUR states about ANY function entity.
> 

https://www.researchgate.net/publication/323268530_Defining_a_Decidability_Decider

-- 
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre 
minds." Einstein

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#38618

On 8/31/21 9:44 AM, olcott wrote:
> On 8/30/2021 11:20 AM, wij wrote:
>> Let function mean a deterministic process, like the function of
>> mathematics
>> https://en.wikipedia.org/wiki/Function_(mathematics)
>> X:X->Y
>> given a function f∈X taking input x∈X and output a deterministic y∈Y.
>> The point here is that X, entity of the function f can be anything,
>> including any super intelligent being who acts as a function, e.g. alien
>> creature, god,...,etc.
>>
>> No function f can decide the property of another function g that g can
>> defy.
>> GUR(v4) https://groups.google.com/g/comp.theory/c/_tbCYyMox9M
>>
>> Thus, the conventional HP is a sub-instance of GUR.
>> This is a more general and much stronger statement than Gödel's
>> incompleteness
>> theorems (mathematical formal system) and Rice's theorem(algorithm),
>> because
>> GUR states about ANY function entity.
>>
> 
> https://www.researchgate.net/publication/323268530_Defining_a_Decidability_Decider
> 
> 

Simple anwser.

By your BaseFact (1)

(1) BaseFacts that contradict other BaseFacts are prohibited

We know that a fundamental Base Fact is that a Halting Machine is one
that reaches a Halting State in a finite number of steps and a
Non-Halting on is one that will NEVER reach such a state if allowed to
execute an unbounded number of steps, and

We know that the Fundamental Definition of a Halting Decider is that it
decides what the computation represented by its input will do.

This implies that ANY 'Theorem' that counters these fundamental facts
must be wrong.

Thus your 'Olcott Halting Theorem' is shown to be PROHIBITED since it
says that the machine H^(<H^>) which is shown to Halt is correctly
decide by that theorem to not halt by the decider H;.

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