XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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.   
      
   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*   
      
   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.   
      
   > the determination of this is the goal of   
   > the Theory of Computability.   
   >   
   > Again, you don't understand what you are talking about, so you get the   
   > wrong definition.   
   >   
   > Part of your problem is that you use words that are so close to being   
   > correct, that by giving you the benefit of the doubt, and then you show   
   > that you got just luck to use words that sounded correct, but you really   
   > didn't know what you were talking about.   
      
      
   --   
   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)