John Edser wrote:
>>>BOH:-
>>>What do you mean by "separate sets"?  What makes them separate?
>>
> 
>>>JE:-
>>>I have previously answered this question
>>>within a post that you did not reply to.
>>> 
>>>In set theory
>>>"what makes them separate" is of no consequence,
>>>because this, like the question of equivalent
>>>set elements, lies outside of pure mathematics
>>>(it is _not_ a proposition of mathematics).  
>>>
>>
>  
> 
>>BOH:-
>>This is the nearest you get to giving an answer, and it's clearly not 
>>much of an answer.
> 
>  
> 
>>JE:-
>>As usual, BOH just snips the answer provided.
>>_Absolute_ separate sets, that contain the
>>_same_ set element type, are assumed to exist
>>within set theory. Obviously, if they could
>>not exist, zero set intersection or union 
>>would now be possible because only single sets with 
>>the same set elements can now exist. In this case, no
>>sets could join or intersect because every separate
>>set must contain different set elements and a set 
>>cannot intersect or join with just itself. 
> 
> 
> BOH:-
> Ah, so are you defining "separate sets" as ones that do not have any 
> elements in common?
> 
> JE:-
> Absolutely separate sets are NOT intersected
> with any other set. I strongly suggest you read 
> an entire post before responding. Obviously, I
> was referring above, to just a hypothetical 
> case that does _not_ exist within set theory,
> where absolutely all sets are only allowed to 
> contain different types of set elements. In this 
> situation no intersection or union is possible 
> (again, very obviously). This being the
> case, absolute separate sets that contain
> the _same_ type of set elements (not necessarily 
> the same number!) have to be able to exist within
> set theory otherwise set theory would be utterly
> useless. PLEASE READ AND CONFIRM YOU UNDERSTAND
> WHAT YOU IGNORED:-

I've read and understood, but I was asking for a definition of "separate 
set", which was not in the excerpt.  However, you have now digen me a 
definition.


>>BOH:-
>>By "separate", do you mean "having no elements in
common"?
> 
> 
>>JE:-
>>No, as I specifically stated, I 
>>referred to absolutely separate sets
>>that contain the _same_ set element 
>>type.
> 
> 
> BOH:-
> The same type of element maybe, but can the actual elements that are of 
> the same type be in both sets?
> 
> JE:-
> Only when they intersect. 
> The whole point of having absolutely
> separate sets that contain the same type
> of set element is to be able to join
> or intersect sets.
> 
That's rather pointless - you've just written that they can't intersect.

> 
>>Again:
>>Please confirm or deny the main proposition
>>under discussion: The logic of natural selection
>>can be validly described as the 100% intersection of
>>all parental sets of total fitness within one population.
> 
> 
> BOH:-
> I'm still trying to find out what you mean.  Until I discover this, I 
> can't give an answer.
> 
> JE:-
> Lets get it right. You are still
> struggling (after how many months?)
> to understand/accept basic set theory that
> is taught to junior high school students.

No, I'm struggling to understand how you apply it to fitness.  I would 
expect any high school student to be able to tell me what are the 
elements in an intersection between two sets the first time I ask them.

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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