Re: Transitive Closure
Date: Mon, 17 May 2004 13:46:19 +0100
Message-ID: <Hu2qc.4347$wI4.496108_at_wards.force9.net>
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.
>
>
> Commutativity does make sense with unary operators.
> M--f-->M--g-->M
> fg = gf or fg != gf
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 - 14:46:19 CEST