Re: set builder notation for relational division

On May 13, 9:18 am, Marshall <marshall.spi..._at_gmail.com> wrote:
> I was trying to come up with a set builder notation description
> of relational division. I didn't like what I had, so I went a-
> googling.
>
> I found this:
>
> A(a,b)
> B(b)
>
> A / B = {(a) | exists (a, b) in A forall (b) in B}

I always was uneasy about those forall - exists constructs, but may I suggest that relational division is

A / B = {(a) | forall (b) in B (a, b) in A}

because both a nd b are already bounded (b by forall quantifier, and a by being at the feft hand side of the set notation)?

> If we want to generalize that, we could say
>
> A(a,b)
> B(b,c)
>
> A / B = {(a, c) | exists (a, b) in A forall (b, c) in B}

Same problem with variable binding. Besides, "forall (b, c) in B" doesn't sound right here. Received on Mon May 14 2007 - 12:28:42 CDT