Re: Transitive Closure

From: Alfredo Novoa <alfredo_at_ncs.es>
Date: 18 May 2004 03:44:20 -0700
Message-ID: <e4330f45.0405180244.9d5d351@posting.google.com>

mikharakiri_nospaum_at_yahoo.com (Mikito Harakiri) wrote in message news:<8a529bb.0405171058.36a5a26_at_posting.google.com>...

> So we are talking about different algebra, that has a universe with
> elements being unary relational algebra operators only -- selection,
> projection,

They are binary operators. Restriction has two operands: a relation and a boolean function, and projection a relation and a set of attributes.

> Cartesian Power (as product is, unfortunately, binary
> operator)

It could be defined as an n-ary operation like: join, semijoin, union, intersection, etc.

*(a,b,c) = *(a,c,b) = *(b,a,c) = *(b,c,a) = *(c,a,b) = *(c,b,a)

>, transitive closure, and, perhaps, negation. In this tiny 4

> element universe we define one binary operation: composition of unary
> relational operators.

Which composition?

> traditional algebra commutativity is all or nothing proposition: it's
> either commutative on the whole universe, or isn't (if there is at
> least a pair of elements such that ab!=ba).

Again a binary operator.

Regards
Alfredo Received on Tue May 18 2004 - 05:44:20 CDT