Re: Sets and Lists, again

"Marshall" <marshall.spight_at_gmail.com> wrote in message news:1148141323.785675.261540_at_u72g2000cwu.googlegroups.com...
> David Cressey wrote:
> >
> > So, at the logical level, why isn't a list just a set of entries with
some
> > natural order implied by one of its attributes?

> Be careful of the idea of "natural order implied by one of its
> attributes."

> It makes it sound as if there is a distinguished order when there
> isn't. (Sort of like picking one key to be the primary key.) Any order
> you can come up with for a relation is just as "natural" as any
> other order. And the existence of an order on an attribute doesn't
> make a relation a list.

> With a list, there *is* a distinguished order, (as well as all the
> other orders possible.)

A list *is* a distinguished order. :-)

> The definition of list is: a target set (relation for our purposes) and
> a mapping from the natural numbers to the set. More useful in
> a programming context is a finite list, in which the mapping is
> from [0..n]. The map and the relation together form the list.

> It is important to be clear about the differences among: set, relation,
> bag, ordered set, ordered bag, list. It's also important to distinguish
> between a total order, a partial order, and a quasi order.

Why insisting of the differences when we can focus on what they have in common ? :-) Received on Mon May 22 2006 - 12:50:05 CEST