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Re: Matheology ? 222 Back to the roots
Posted:
Mar 1, 2013 9:58 AM


On 01/03/2013 3:11 AM, Alan Smaill wrote: > Nam Nguyen <namducnguyen@shaw.ca> writes: > >> 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 '^'. > > Who said that that is a predicate here?
In a structure, a function is a special predicate: all of which are just _sets of ntuples_ .
> >> 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? > > It fits with Shoenfield in the case where the only predicate > is equality.
As just mentioned, you still have to construct that special predicate set for the symbol '^'. To be precise of course.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 



