Date: Mar 1, 2013 1:25 AM
Author: namducnguyen
Subject: Re: Matheology ? 222 Back to the roots

On 28/02/2013 11:15 PM, Virgil wrote:
> 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.


Then a) you should have removed "sci.logic" from the list,
and b) should not have asked me to "give us your textbook definition
of structure and show why the above fails to meet it". You asked
for it and I've answered it: and you were wrong in your original
statement.


--
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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
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