John Edser wrote:
>>>>BOH:- 
>>>
>>>>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).
>>>
> 
>>>>JE:-
>>>>Only _equivalent_ set elements are in n set
>>>>intersections and not "the same" set element.
>>>
> 
>>>BOH:-
>>>Having given you the quotes, I was hoping you would actually comment on 
>>>them, rather than continue on about equivalence.  It's simply not a 
>>>matter of whether elements are equivalent - it's whether a matter of 
>>>which sets that are members of.
>>
> 
>>
> 
> 
>>>JE:-
>>>I have commented on the quotes, in detail.
>>>For example, "set C of all elements that 
>>>are in both A and B" means that all the
>>>set elements in the intersection C are strictly
>>>_equivalent_ elements and not just elements
>>
>>>from one set, i.e not "the same" elements.
> 
> 
>>BOH:-
>>This is opaque to me.  Are you saying that the elements in the 
>>intersection C are not also in sets A and B?
> 
> 
>>JE:-
>>The concept of equivalence is simple.
>>Two things may be defined equivalent.
>>This does not make them the one, same,
>>thing, but it does mean either of them
>>can represent the other. All I am saying 
>>is that the elements in intersection C are equivalent
>>set elements to the set elements in set A and B.
> 
> 
> BOH:-
> Now can you answer my question - are you saying that the elements in the 
> intersection C are not also in sets A and B?
> 
> JE:-
> All the elements in the intersection C are also in sets 
> A and B. 

Thank you.  After many months, you finally say this.  Just to check, 
does this means that you do agree with the following definitions of 
intersection (copied from a few days ago):
  "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).

Because all the set elements within the intersection
> are defined equivalent nobody knows, and nobody is required to
> know, where the set elements represented within the intersection 
> originated from. 
> 
> You refuse to make any shift from abstract set elements
> to set elements that are defined as biological entities.

Because I had to make sure we both meant the same thing - there's no 
point in talking about the biology if we're using different mathematical 
languages.

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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