Re: Relation subset operators
Date: Sat, 6 Jun 2009 18:16:13 -0700 (PDT)
Message-ID: <b881c994-90bd-40ff-abfd-24fcd8d7fbec_at_h11g2000yqb.googlegroups.com>
On Jun 6, 2:19 pm, vadim..._at_gmail.com wrote:
> The other curiosity is how many different RL expressions
> one can generate with inversions and complements alone. For example,
> the identities
>
> x``` = x`.
> x'' = x.
> x`'`'`'=x`'.
> x'`'`'`=x'`.
>
> show some limitations, but what about less obvious interleavings of
> inversion and complement?
Neither complement (x') nor double inversion (x``) change the header of an input relation. Therefore, they are set operations affecting relation tuples only. Complement (x') is the set complement, and double inversion (x``) is a closure:
(x``)`` = x``.
I vaguely remember an exercise in Kuratovski and Mostovski "Set Theory" book that asserts that starting with an arbitrary set one can build no more than 13 different sets by interleaving application of closure and complement. Received on Sun Jun 07 2009 - 03:16:13 CEST