Re: Stored fields ordered left to right

"Dawn M. Wolthuis" <dwolt_at_tincat-group.com> wrote in message <news:bsj14k$hcs$1_at_news.netins.net>...

> "Joe "Nuke Me Xemu" Foster" <joe_at_bftsi0.UUCP> wrote in message
> news:1072496216.517226_at_news-1.nethere.net...

> > A tuple is a set of ordered pairs of the form (attribute, value).
> > Defining an ordering for the attributes would be superfluous.
> >
> > URL:http://en2.wikipedia.org/wiki/Ordered_pair
>
> So a tuple is NOT ordered? Why not? Why even call an unordered set a
> tuple? Tuples imply ordering, right? They are elements of Set1 x Set2 x
> Set3 x ... Setn. It is fine with me if you want those sets to be sets of
> ordered pairs -- they can be sets of whatever, but the relation is then a
> set of tuples (s1, ... sn) where s1 is an element of S1 (and in your def,
> that means it would be an ordered pair).
>
> But a RELATION itself is a set of ORDERED TUPLES -- RIGHT? Else please
> point me to a MATHEMATICS definition that allows for relations that are not
> ordered. I'm not finding any such definitions.

Yes, a "relation" built from ordered n-tuples would be quite broken! Consider an ordered 4-tuple, (a, b, c, d), or, { {a}, {a, b}, {a, b, c}, {a, b, c, d} }. What would happen if any two attributes were *equal*? A set of ordered pairs, OTOH, wouldn't lose information if any or all of its ordered pairs collapsed to sets containing just a single element. Even if {{{a}, {a, a0}}, {{b}, {b, b0}}, {{c}, {c, c0}}, {{d}, {d, d0}}} collapses to just { {a}, {b}, {c}, {d} } you could still figure out what was what. It's a good thing relational tuples aren't ordered n-tuples!

--
Joe Foster <mailto:jlfoster%40znet.com>  Sign the Check! <http://www.xenu.net/>
WARNING: I cannot be held responsible for the above        They're   coming  to
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