Date: Mar 1, 2013 1:54 AM
Author: Virgil
Subject: Re: Matheology ? 222 Back to the roots

In article <lRXXs.97523$Ln.54803@newsfe22.iad>,
Nam Nguyen <namducnguyen@shaw.ca> wrote:

> On 28/02/2013 11:15 PM, Virgil wrote:
> > In article <G8VXs.46028$Q91.31634@newsfe26.iad>,
> > Nam Nguyen <namducnguyen@shaw.ca> wrote:
> >

> >> On 28/02/2013 7:51 PM, Virgil wrote:
> >>> In article <khUXs.345339$pV4.177097@newsfe21.iad>,
> >>> Nam Nguyen <namducnguyen@shaw.ca> wrote:
> >>>

> >>>> On 28/02/2013 8:27 AM, Frederick Williams wrote:
> >>>>> Nam Nguyen wrote:
> >>>>>>
> >>>>>> On 27/02/2013 10:12 PM, Virgil wrote:

> >>>>>>> In article <R8AXs.345282$pV4.85998@newsfe21.iad>,
> >>>>>
> >>>>>>> The set of all functions from |N = {0,1,2,3,...} to {0,1,2,...,9} with
> >>>>>>> each f interpreted as Sum _(i in |N) f(i)/10^1, defines such a
> >>>>>>> structure..

> >>>>>>
> >>>>>> That doesn't look like a structure to me. Could you put all what
> >>>>>> you've said above into a form using the notations of a structure?

> >>>>>
> >>>>> There is a set and a collection of functions on it. How does it fail to
> >>>>> be a structure?

> >>>>
> >>>> From what textbook did you learn that a structure is defined as
> >>>> "a set and a collection of functions on it"?

> >>>
> >>> Then give us your textbook definition of structure and show why the
> >>> above fails to meet it.

> >>
> >> Shoenfield, Section 2.5 "Structures". One reason the above fails is,
> >> you don't define, construct, the predicate (set) for the symbol '^'.
> >>
> >> And that's just 1 reason amongst others. Do you admit it now that
> >> the above fails to meet the requirements of a language structure?

> >
> > No, though it may not satisfy your requirements, it satisfies mine well
> > enough to go on with.
> >
> > Sci.math is not as formal as Principia Mathematica.

>
> Then a) you should have removed "sci.logic" from the list,
> and b) should not have asked me to "give us your textbook definition
> of structure and show why the above fails to meet it". You asked
> for it and I've answered it: and you were wrong in your original
> statement.


Only in your opinion.
--