# curiousity of sets of no relations?

Date: Sat, 10 Jun 2006 15:26:43 GMT

Message-ID: <TwBig.7169$IK3.4057_at_pd7tw1no>

In his Intro to DB, 8th Ed., page 195 in the Relational Algebra chapter, CJ Date says:

(Quote, with point numbers added and asterisks for footnotes)

Some Generalizations

(2) If s contains no relations at all, then:

(2.1) The join of all relations in s is defined to be TABLE_DEE (the

identity with respect to join).

(2.2) The union of all relations in s is defined to be the empty

relation of type RT.

In the exercises for that chapter (#7.10), Date asks "Given that intersect is a special case of join, why do not both operators give the same result when applied to no relations at all?"

My guess at the motivation for all this is that it is at least partly to define things completely enough to allow prefix notation, eg. JOIN/INTERSECT/UNION (r1, r2, ... , rn). If that's so, then I can see that we would want JOIN() (by this I mean the JOIN of nothing) to give TABLE_DEE, if we wanted (JOIN())JOIN(r1) to give r1. Similarly for INTERSECT() and other combinations of the three operators.

That seems a practical motivation. In terms of relations and/or set theory/predicate calculus can anybody give a more theoretical one?

p Received on Sat Jun 10 2006 - 17:26:43 CEST