Re: Objects and Relations

On Jan 30, 7:41 pm, "Neo" <neo55..._at_hotmail.com> wrote:
> > > > > > > what is a relational expression for the string bob?
> > > > > > { (0, 'b'), (1, 'o'), (2, 'b') }
> > > > > Is the following relationally equivalent?
> > > > > { (2, 'b'), ('b', 0'), ('o', 1) }
>
> > > > No. The parenthesized elements within the braces can be reordered;
> > > > the elements of the ordered tuple within the parentheses cannot.
>
> > > What is the logic/proof/rationale that allows one
> > > to go from sets with unordered elements to sets with ordered element?
>
> > We do not create a new kind of set.
> > Rather, we use one set to model the order of another set.
>
> I still can't understand the logic/rationale explaining the transition
> from sets with unordered elements to sets with ordered elements,
> either from above or Chapter 7 of Schuam's Outline.

Hint: there *are no* sets with ordered elements. There are sets of unordered elements, and there are *other* sets of unordered elements that contain information that specifies an order for another set.
*All* of the sets involved are unordered.

Here's a set: R = { 3, 1, 2}. It is equal to this set: {1, 3, 2}. Etc.

Here's an (unordered!) set that describes an order to the above set:

O = {

(1, 2),
(2, 3),
(1, 3)

The *pair* (R, O) are sometimes called a "totally ordered set" even though the pair itself is not a set! Wacky, huh?

> If unordered sets are the foundation, how can one express the string
> 'bob' with unordered sets only?

I already showed that in a previous post.

Marshall Received on Wed Jan 31 2007 - 06:24:07 CET