# Re: What databases have taught me

Date: 1 Jul 2006 11:29:38 -0700

Message-ID: <1151778578.203807.299950_at_m79g2000cwm.googlegroups.com>

- 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?

> > > What is important is not which operations we consider

*> > > 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