Re: General Form of Relationships?

Neo wrote:
>
> > The most general way to view a "relationship" among a set of n variables
> > is as an arbitrary subset of n-space. (In your examples, the variables
> > may come from other sets S_1, ..., S_n instead of the real number line,
> > in which case a "relationship" is a subset of the cartesian product
> > S_1 x S_2 x ... x S_n .)
>
> I didn't state my question clearly but your post triggers an idea.
> Suppose the x-axis represents a set of balls and the y-axis a set of
> colors, then a dot at x,y would indicate "ball2 is Red". How to extend
> this system to represent "ball between box and chair"? Could I suppose
> 3-axes where each represents the set of all things in a room. Then a
> dot a x,y,z would indicate what thing is between two other things?

Since David hasn't answered: yes, but.

R(a,b,c...) iff the point (a,b,c,...) lies in a certain subset of A x B x C x... . You can view that subset as being the relation (one does in set theory.) The 'but' is that you won't want A, B, C,... just to be real numbers which might be what your use of 'x-axis' implies. (Btw, I didn't use 'x' as a variable because I wanted to use it for Cartesian product.)

GC Received on Sun Jun 22 2003 - 00:17:33 CEST