Date: Mar 1, 2013 1:15 AM
Author: Virgil
Subject: Re: Matheology ? 222 Back to the roots

Nam Nguyen <namducnguyen@shaw.ca> wrote:

> On 28/02/2013 7:51 PM, Virgil wrote:
> > 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:

> >>>
> >>>>> 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.
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