XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/24/2025 3:38 PM, Richard Damon wrote:   
   > On 12/24/25 3:56 PM, olcott wrote:   
   >> On 12/24/2025 2:33 PM, Richard Damon wrote:   
   >>> On 12/24/25 3:11 PM, olcott wrote:   
   >>>> On 12/24/2025 1:28 PM, Richard Damon wrote:   
   >>>>> On 12/24/25 2:20 PM, olcott wrote:   
   >>>>>> *This defines the scope of computation*   
   >>>>>> A Turing-machine decider is a Turing machine D that   
   >>>>>> computes a total function D: Σ∗ → {Accept,Reject},   
   >>>>>> where Σ∗ is the set of all finite strings over the input   
   >>>>>> alphabet. That is:   
   >>>>>>   
   >>>>>> 1. Totality: For every finite string input w ∈ Σ∗, D   
   >>>>>> halts and outputs either Accept or Reject.   
   >>>>>>   
   >>>>>> *This is semantically entailed from this definition*   
   >>>>>> Any requirement that requires more than the above   
   >>>>>> definition can provide is a requirement that is outside   
   >>>>>> of the scope of computation.   
   >>>>>>   
   >>>>>   
   >>>>> FALSE, proving you don't understand the meaning of "Scope".   
   >>>>>   
   >>>>   
   >>>> Instead of spouting off dogma any idiot can do   
   >>>> that, you define what you think that the term   
   >>>> "scope of computation" actually means.   
   >>>   
   >>> You are using the wrong term.   
   >>>   
   >>> It is the Scope of the Theory of Computation, which is the list of   
   >>> problems that we are allowed to ask a Turing Machine/Computation to   
   >>> try to compute.   
   >>>   
   >>> That list of problems is ANY mapping of a source domain (expressed to   
   >>> the machine via some representation) to an answer domain (again   
   >>> expressed via some representaiton)   
   >>>   
   >>>>   
   >>>> This is what Google AI said.   
   >>>> The "scope of computation" refers to the range   
   >>>> and limits of what can be solved or processed   
   >>>> using algorithms and computational methods.   
   >>>>   
   >>>> That is what I mean. What do you mean?   
   >>>>   
   >>>   
   >>> Which isn't the Scope of the Theory of Compuation, but a descption of   
   >>> what is actually computable,   
   >>   
   >> The scope of computation is the boundary of   
   >> what is and what is not computable.   
   >   
   > Which is NOT the boundry of what you can ask of a decider, as it is   
   > allowed for the Function to not be computable.   
   >   
   > You are confusing the boundary of ABILITY with the boundry of allowed   
   > REQUIREMENT.   
   >   
      
   You are confusing that requirement can exceed an ability.   
   Some idiot could "require" the a Turing Machine to   
   compute the last digit PI.   
      
   >>   
   >> Turing machine deciders: Transform finite string   
   >> inputs by finite string transformation rules into   
   >> {Accept, Reject} values.   
   >>   
   >> *Translated into this formal specification*   
   >>   
   >> *DEFINE the actual limits of computation*   
   >> *DEFINE the actual limits of computation*   
   >> *DEFINE the actual limits of computation*   
   >   
   > Of what is COMPUTABLE, not what can be asked to try to compute.   
   >   
      
   Asking it try try to compute anything outside the   
   scope of computation is nuts.   
      
   >>   
   >> A Turing-machine decider is a Turing machine D that   
   >> computes a total function D :  Σ∗ → {Accept,Reject},   
   >> where Σ∗ is the set of all finite strings over the   
   >> input alphabet. That is:   
   >   
   > And, to be an XXXX Decider, must produce the mapping of the XXXX function,   
   >   
      
   Not when no such mapping exists as transformations   
   from finite string INPUTS INPUTS INPUTS INPUTS   
   INPUTS INPUTS INPUTS INPUTS   
   INPUTS INPUTS INPUTS INPUTS   
   INPUTS INPUTS INPUTS INPUTS   
   According to the specification of the limits of computation.   
      
   > Sorry, you are just proving you are too stupid to understand what you   
   > are talking about.   
   >>   
      
   It is not me that is too stupid here.   
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)