Re: What databases have taught me
Date: 1 Jul 2006 11:29:38 -0700
- All of us agree that there is an unlimited number of consistent operations O that can be defined on a set S.
- All of us agree that mathematicians and others often distinguish a subset OA of O as 'axioms'.
Let us call OD = O - OA 'derived' operations. And let us call a subset OS of OD 'scoped' operations which are operations that are currently "in scope".
3a) I (and Marshall?) say that S + OA defines a data type T. 3b) You (Bob) say that S + O defines a data type T. 3c) Dmitry says that S + OA + OS defines a data type T.
Do you Bob, Marshall, and Dmitry find this summary accurate?
> > > fundamental and which we consider auxiliary. What is
> > > important is all of those operations exist and we can
> > > communicate them to each other.
> > Not important? Well that is a large part of mathematics,
> > finding sets of operations (the smaller the better) we
> > consider fundamental and from which we can derive other
> > operations.
> Axiomatization is arbitrary. Mathematicians also spend
> time trying to find completely different sets of axioms
> for the same things and then trying to prove the
> equivalence between them.
- Keith -- Fraud 6