John Edser wrote:
>>>>JE:-
>>>>Also, I have no idea what
>>>>"separate  sets don't" was 
>>>>actually referring 
>>>>to in your previous reply.
>>>
> 
>>>BOH:-
>>>Try reading it as an answer to your post.  I'm saying that separate sets 
>>>don't intersect.
>>
> 
>>>JE:-
>>>Would _please_ write out (as I
>>>_previously_ requested) the definition 
>>>you said I had given, and then derive 
>>
>>>from that definition "that separate sets 
>>
>>>don't intersect"  so we can understand 
>>>what exactly you are referring to.
>>
> 
>>BOH:-
>> From the 7th of November:
>>"Absolutely separate sets are NOT intersected with any other set."
> 
> 
>>JE:-
>>Note that this does not exclude
>>absolutely separate sets from
>>intersecting.
> 
> 
> BOH:-
> How can they intersect if they are not intersecting?  You're not making 
> any sense.
> 
> JE:-
> This just Mad Hatter Nonsense.
> Separate sets do not have to remain
> non intersected or not joined.
> The point of having them absolutely
> separate is to be able to intersect
> or join them up if and only if,
> they contain the same type of
> set elemts. Where in this discussion
> did I claim that absolutely
> separate sets "intersect if 
> they are not intersecting"?!?
> 
That's not what I claimed you wrote.

> 
>>>JE:-
>>>I agree that absolute separate
>>>sets don't intersect. Do you agree
>>>that absolute separate sets can however,
>>>contain the same type of set element?
>>
>  
> 
>>BOH:- 
>>I've never had any problem with that - it's your claim that they contain 
>>the same actual elements (i.e. that they have a non-empty intersection) 
>>that I have trouble with.
> 
> 
>>JE:-
>>Intersecting sets only contain the same
>>_type_ of element. I have never claimed
>>they contain the same actual elements.
> 
> 
> BOH:-
> Alas, you have by claiming that you're using the usual mathematical 
> concept of intersection.  
> 
> JE:-
> "The usual mathematical 
> concept of intersection" does NOT
> claim that intersecting sets 
> contain the same _actual_ elements,
> it simply claims they are _equivalent_.

Rubbish.  See below.


> 
> BOH:-
> If you're not doing this, then please 
> acknowledge this and tell us what your definition is.
> 
> If you want some proof that I'm using the accepted definition of 
> fitness, then look at these sites:
> http://whatis.techtarget.com/definition/0,,sid9_gci838379,00.html>
> http://www.shu.edu/projects/reals/logic/defs/sets.html>
> http://www.quantnotes.com/fundamentals/backgroundmaths/settheory.htm>
> (definition 2)
> 
> JE:-
> Please provide the quote from the 
> above that substantiates your amazing
> claim that the elements within 
> the intersection are absolutely
> the same element and not just 
> equivalent elements?
> 
 From the first site:
"Given two sets A and B, the intersection of A and B, written A INT B, 
is the set C of all elements that are in both A and B."
 From the second site:
"A INT B: A intersection B is the set of all elements that are in both 
sets A and B."
 From the third site:
"Intersection - Denotes the set of elements that are members of all the 
sets under consideration."
(I've written INT for the intersection symbol, as it doesn't appear in 
ASCII).

Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
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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