On 5/29/2012 11:46 PM, Jesse Mazer wrote:
On Tue, May 29, 2012 at 10:49 PM, Stephen P. King
<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:
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
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 sense.
You previously wrote: "The notion of "choosing" isn't actually
important--if a proof says something like "pick an arbitrary member of
the set X, and you will find it obeys Y", this is equivalent to the
statement "every member of the set _X obeys Y_"." and not " "an
arbitrary member of set Y will have property X" just means "every member
of set Y has property X" ", a small but possibly important difference.
Are you assuming a commutative relation for Y and X? Details...
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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