String negative indices?

[Steven D'Aprano]

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