John writes:

>I would be grateful if Dr Atmar would please confirm or deny that
>natural selection can be validly visualised as a 100% intersection
>between all sets of total parental fitness, within one population?

Unfortunately, I haven't been paying much attention to this thread, thus I'm
unsure what is even being asked.

However, Bob writes:

>But you can get green apples and red apples, and both are apples, i.e. 
>are members of the set of apples, but they are clearly not equivalent. 
>They are also members of the sets of green and red fruit as well.  The 
>fact that an an apple is green means that it is in the intersection of 
>apples and green fruit.

Unfortunately, that's not how a set is defined. The elements -- the equivalent
items within a collection that comprises a set -- are defined either by
explicitly listing each item or by defining a "method." 

A method-defined set is generally written as:

     S = { x : P(x) }

where P(x) is said to be a property of x. Such a property might be absolute
value of the integer numbers, thus the numbers -1 and 1 -- which are
distinguishable items at some lower level (the equivalent of red and green
apples) -- now comprise just one element of the set S. 

If the set was the set of all fruit, apples might be only one element,
depending on the coarseness of the defining methodology. Varieties, color,
shape, ripeness could all be characteristics that might separate out the
individuals at a finer grain of knowledge but which are now indistinguishable
and unknowable at the level the set is defined.

The same is just as true for the set of all mammalian species. The methodology
that defines these species might be some form of cluster-centric
phylogenetic/cladistic  DNA analysis. At this level of set determination, the
weight, height and color of the individuals that comprise an element of the set
(a species x in the set S of all mammalian species) is unknown and irrelevant.

Wirt Atmar
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