Re: Clean Object Class Design -- Circle/Ellipse
Date: 18 Aug 2001 12:22:44 -0700
Message-ID: <bdf69bdf.0108181122.3d91af67_at_posting.google.com>
marc.gluch_at_mindtap.com (Marc Gluch) wrote in message news:<3b769e09.3207460634_at_news.grpvine1.tx.home.com>...
>
> Definition 1 (Gluch)
> S is a subtype of T iff S has all axioms of T plus some additional
> one(s).
Marc,
According to this definition neither integers is subtype of reals, nor the other way, right? (If we take Peano axiom system for positive integers, and compare it with definition of real number system as an algebraic structure represented by Dedekind-complete ordered field, then it is easy to see that induction axiom doesn't hold for real numbers, while multiplicative closure doesnt hold for integers). Therefore, could you suggest some examples demonstrating the utility of your definition?
Also, your definition seems to ignore subtle effects like axiomatic incompleteness of the mathematical model (as if we don't have enough confusion already;-). Received on Sat Aug 18 2001 - 21:22:44 CEST