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Question about algorithm numerical domain

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  Question about algorithm numerical domain programmernovice <ivandenisovich826@gmail.com> - 2018-04-30 11:09 -0700
    Re: Question about algorithm numerical domain Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-04-30 19:38 +0100
      Re: Question about algorithm numerical domain programmernovice <ivandenisovich826@gmail.com> - 2018-05-01 08:58 -0700

#8735 — Question about algorithm numerical domain

Hi everyone. My book (Smith's "An Introduction to Goedel's Theorems") defines the numerical domain of an algorithm as the set of naturals that, when input individually to the algorithm, result in its "working", that is to terminate and output some result. In the book it is also stated that any wff of a programming language (e. g. C++) can be considered an algorithm, having a numerical domain.

I'm not clear about how an instruction such as "Go To" can be considered an algorithm, or if it is, then how does one determine its numerical domain. 

Can someone please explain this? All help greatly appreciated.

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#8736

programmernovice <ivandenisovich826@gmail.com> writes:

> Hi everyone. My book (Smith's "An Introduction to Goedel's Theorems")
> defines the numerical domain of an algorithm as the set of naturals
> that, when input individually to the algorithm, result in its
> "working", that is to terminate and output some result. In the book it
> is also stated that any wff of a programming language (e. g. C++) can
> be considered an algorithm, having a numerical domain.
>
> I'm not clear about how an instruction such as "Go To" can be
> considered an algorithm, or if it is, then how does one determine its
> numerical domain.

Quite.  But then it almost certainly does not come under the definition
of "WFF of a programming language".  A goto hidden in a function, f, is
OK because we can consider f(x) to be WFF with a numerical domain.

-- 
Ben.

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#8738

On Monday, April 30, 2018 at 1:38:13 PM UTC-5, Ben Bacarisse wrote:
> programmernovice writes:
> 
> > Hi everyone. My book (Smith's "An Introduction to Goedel's Theorems")
> > defines the numerical domain of an algorithm as the set of naturals
> > that, when input individually to the algorithm, result in its
> > "working", that is to terminate and output some result. In the book it
> > is also stated that any wff of a programming language (e. g. C++) can
> > be considered an algorithm, having a numerical domain.
> >
> > I'm not clear about how an instruction such as "Go To" can be
> > considered an algorithm, or if it is, then how does one determine its
> > numerical domain.
> 
> Quite.  But then it almost certainly does not come under the definition
> of "WFF of a programming language".  A goto hidden in a function, f, is
> OK because we can consider f(x) to be WFF with a numerical domain.
> 
> -- 
> Ben.

Thanks for your reply.

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