On Sat, 24 Jun 2006 21:15:17 -0700, Erik Max Francis wrote: > Steven D'Aprano wrote: > >> In mathematics, well, maybe... certainly in the Real number system, there >> is no difference, and +0 and -0 are just two ways of writing the same >> thing. In the hyperreals, +0 and -0 are the same, but there are >> infinitesimals which are different, and signed. I don't know enough about >> the surreals to comment. In matrix maths, there are an infinite number of >> different matrices where all the elements are zero -- they are all >> distinct, different, zeroes. > > What do you even mean by that? By "matrix maths," do you just mean > matrices whose elements are reals, or something else?
Given any matrix M, there is a matrix Z such that M+Z = M. That matrix Z is equivalent to zero in the reals, where x+0 = x. In the reals, there is only one "zero", 0. In matrices, there are an infinite number of "zeroes": 1x1 matrix: [0] 1x2 matrix: [0 0] 1x3 matrix: [0 0 0] 2x2 matrix: [0 0] [0 0] etc. It is true that none of these are exactly equivalent to +0 and -0, but my point was that there can be more than one distinct zero in pure mathematics, and there is nothing wrong with the concept of a system with more than one distinct zero. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
