John Edser wrote:
>>>>JE:-
>>>>________________________________________________
>>>>If set intersection is just a _property_,
>>>>exactly what _process_ is it just a property
>>>>of?
>>>>________________________________________________
>>>
> 
>>JE:-
>>...is "the nub of the problem" but NO "I am
>>not "the only person who thinks this is true". Do you 
>>disbelieve the evidence set before you? Can you not see 
>>that the intersection between set A = 3 and set B = 5
>>has 4 possible self _exclusive_ levels of set intersection?
> 
> 
> BOH:-
> No.  Can you tell me of any other person who can?  Name names!
> 
> JE:-
> Godel determined that mathematics
> is not self consistent. 


Now can you answer the question.


>>JE:-
>>You simply did not understand the definition you supplied.
>>Mathematics is applied logic. An application of logic within 
>>mathematics produces a set property. Mathematics is therefore,
>>limited by the logic being applied to it. Mathematics cannot 
>>determine which of many possible logical processes are being applied 
>>within mathematics at any moment. Yes, the intersection has
>>"all elements that are in both A and B" but as we have seen 
>>when set A = 3 and set B = 5 four different self exclusive set 
>>intersections can exist and not just one, where in every case it remains
>>true that the intersection contains "all elements that are in both A 
>>and B" depending entirely on how you define a minimum of two points 
>>of commonality.
> 
> 
> BOH:-
> Huh?  But which one of the intersections actually does exist is 
> determined by which of the elements IS a member of both sets. 
> 
> JE:-
> Yes, but this has 4 possible outcomes and not just
> one outcome given A=3 and B=5. _Each_ of the 4
> outcomes _satisfies_ the definition DEPENDING
> on "a minimum of two points of commonality".
> 
Actually, if set A=5 and set B=3 then the intersection is empty, because 
5!=3....

I assume you mean that A has 5 elements and B has 3.  But that is not 
enogh to define the sets A and B.

> 
>>snip<
> 
> BOH
> Note that with your A's and B's, you have not defined what the elements 
> are. 
> 
> JE:-
> Mathematic defines set elements as numbers. 

Rubbish.  Set elements are set elements.  They may be numbers, letters, 
  fitness elements or elephants.  The point is that the relationship 
between the elements is determined by their set memberships.

Bob

-- 
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
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