
Re: Cross product
Posted:
Apr 14, 2012 9:02 PM


The phrase "cross product" normally means the product of two vectors and that is what Angela Richardson is referring to. But you say the "cross product of two sets" which makes me think you mean the CARTESIAN product.
If so, you will need to specify what you mean by "the same as". If A= {a, b}, B= {u, v}, and C= {x, y}, then AXB= {(a,u), (a,v), (b,u), (b, v)} while BXC= {(u, x), (u, y), (v, x), (v, y)} so that (AXB)XC= {((a,u),x), ((a,v),x), ((b,u),x), ((b, v),x),(z((a,u),y), ((a,v),y), ((b,u),y), ((b, v),y)}} while AX(BXC)= {(a,(u, x)), (a,(u, y)), (a,(v, x)), (a,(v, y),(b,(u, x)), (b,(u, y)), (b,(v, x)), (b,(v, y))}
While there is an obvious EQUIVALENCE between the two sets, they are NOT equal.

