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Topic: Matheology ? 222 Back to the roots
Replies: 3   Last Post: Mar 1, 2013 9:58 AM

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namducnguyen

Posts: 2,699
Registered: 12/13/04
Re: Matheology ? 222 Back to the roots
Posted: Mar 1, 2013 9:58 AM
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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 n-tuples_ .

>
>> 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
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