Date: Mar 1, 2013 2:31 PM
Author: Frederick Williams
Subject: Re: Matheology ? 222 Back to the roots
Nam Nguyen 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 '^'.

One might define a particular structure as having universe {0,1,2,...}

and one relation R such that

R(x,y,z) iff x = y^x.

_That_ defines a structure in Shoenfield's sense, there is no need to

say what '^' means.

--

When a true genius appears in the world, you may know him by

this sign, that the dunces are all in confederacy against him.

Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting