Re: Objects and Relations

On Jan 30, 6:33 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.
>
> I assume you would say that sets with unordered elements are the
> foundation. If so, how does this let one create a new type of set with
> ordered elements? What is the proof that the new type of set is firmly
> based on the foundation? What is the logic/reationale that allows one
> to go from sets with unordered elements to sets with ordered element?
> What logic prevents one from creating another new type of set with his
> own rules?

I believe you have Schaum's Outlines on Set Theory and Related Topics on your shelf, yes? Chapter 7 describes this in detail.

In brief:

We do not create a new kind of set. Rather, we use one set to model the order of another set. In standard mathematics (if there is any such thing) it is done with ordered pairs and sets only.

Marshall Received on Wed Jan 31 2007 - 03:42:31 CET