Re: Transitive Closure

x wrote:

>>The commutative property does not make sense with unary operators like
>>TClose. Unary operators are always commutative because there is only
>>one operand's order.

I think the confusion here is that in something like group theory we say a binary operator "*" is commutative if a*b = b*a. Or writing it as a function we say:

*(a,b) = *(b,a)

What we're talking about here which I think is what Alfredo is misunderstanding is commutativity of the "composition of operators" operator. So say we have unary operators f and g we can define the operator "f*g" to be:

(f*g)(x) = f(g(x)) for all x.

Commutativity of this "*" operation just means that:

f*g = g*f

ie. f(g(x)) = g(f(x)) for all x.

For this to make sense f and g must take arguments of the same type, and return values of that same type as well.

Paul. Received on Mon May 17 2004 - 07:46:19 CDT