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. --
