# Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?

Date: Mon, 17 Feb 2003 15:42:26 -0800

Message-ID: <0xe4a.16$7H6.165_at_news.oracle.com>

"Steve Kass" <skass_at_drew.edu> wrote in message
news:b2rqnp$1tj$1_at_slb2.atl.mindspring.net...

> >The biggest problem with (x,y)={{x},{x,y}} definition is that it's not

*> >associative:
**> >
**> ><a,<b,c>> != <<a,b>,c>
**> >
**>
**> What isn't associative? What does <> represent?
**> What does it mean for a definition to be associative?
**> Associativity is a property of binary operations. What
**> binary operation are you talking about here?
*

I'm sorry: copy and paste typo. I meant

(a,(b,c)) != ((a,b),c)

*> Huh? Many definitions are possible, of course. We could represent
*

> (x,y,z) in any of these ways, I think (I'm sure I messed up the

*> brackets, though):
**> {{1,{x}},{2,{y}}, {3,{z}}
*

You have to define 1, 2, 3, first. Assuming

1={{}}

2={{},{{}}}

And substitution into your definition, you'll get yet another difinition for an ordered pair:

(a,b) = {{{{}},{a}},{{{},{{}}},{b}}}

> {{x},{y,{y}},{z,{z},{{z}}}}

*> {{x},{x,{y,{y,z}}}} -- This is the one I'd call the most natural
*

extension.

> {{x,{x,y}},{{x,{x,y}},z}} -- This is the alternative that bothers you..

This is just a series of random definitions, well spiced with curly bracketed symbols. Or is there any wonderful theory about it? Where in math did you see "We have 10 unrelated alternative definitions, pick anyone you like"? Received on Tue Feb 18 2003 - 00:42:26 CET