On 5/29/2012 11:46 PM, Jesse Mazer wrote:

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On Tue, May 29, 2012 at 10:49 PM, Stephen P. King<stephe...@charter.net <mailto: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 arbitrarymember of set Y will have property X" just means "every member of setY has property X", nothing more complicated. For example, Y might bethe set of all triangles in Euclidean geometry, and X might be theproperty of having all the inner angles add up to 180 degrees. Itwould be easier to understand your question if you similarly suppliedsome simple of what Y, y, j, X, and x could stand for, such that yourdescription above would make sense.Jesse --

Hi Jesse,

`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... -- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.