Re: Relation subset operators
Date: Sat, 6 Jun 2009 12:54:54 -0700 (PDT)
> In relational algebra, I know of only two contexts for the empty set,
> one is the empty heading/attribute set, the other is the empty
> relation/tuple set. The first has two values, the second can have many
> values. Neither operates like arithmetical zero, for example division
> by the empty set is defined whereas it is undefined for zero.
I disagree with the assertiion that division is undefined for zero. The tool of limits demonstrated that the operation is simply not possible because the result would an infinite value that can not be handled solely though mere algebra. I used the example of the zero because this is how I perceive algebric rigor: the need for qualifying a tool and the limits of such tool to be a reliable way to achieve demonstrative properties. As for the empty set, describing some characteristics does not determine it usefulness. I just wished I had your optimism on that.
> I'm not
> sure what "questions" remain unanswered, as far as I know both empty set
> contexts are defined and both function as identities that give
> relational closure, unlike arithmetic.
I believe in the test of time. zero has now been around for more than a millenia and allowed great progress for humanity. I would not say I am confident that the concept of empty set (at least as currently defined) would provide as much to advance research. Hard to say. Received on Sat Jun 06 2009 - 21:54:54 CEST