On Tue, May 29, 2012 at 10:49 PM, Stephen P. King <stephe...@charter.net>wrote:

> Hi Jesse,
>    Would it be correct to think of "arbitrary" as used here as meaning "
> some y subset Y identified by some function i or mapping j that is not a
> subset (or faithfully represented) in X, yet x => y : x /subset X"? The
> "choice" of a basis of a linear space comes to mind. The idea is that one
> it is not necessary to specify the method of identification ab 
> initio<http://en.wikipedia.org/wiki/Ab_initio>
> .

I can't really tell what you're asking here. As I said, "an arbitrary
member of set Y will have property X" just means "every member of set Y has
property X", nothing more complicated. For example, Y might be the set of
all triangles in Euclidean geometry, and X might be the property of having
all the inner angles add up to 180 degrees. It would be easier to
understand your question if you similarly supplied some simple of what Y,
y, j, X, and x could stand for, such that your description above would make


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