```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 tosay 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
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