Re: Transitive Closure

Alfredo Novoa wrote:
>>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:
>
> So "*" is a binary operation.

Yes, * here is a binary operator, but f and g are necessarily unary operators.

It's a bit confusing here because we have two levels of operators. The standard ones that we call here f and g, and what you might think of as a "meta-operator", *.

"*" operates on operators, as well as being an operator itself. It maps two operators to a third operator.

Probably too many uses of the word "operator" here, but I can see where the misunderstanding is.

Paul. Received on Tue May 18 2004 - 07:18:15 CDT