Re: Clean Object Class Design -- Circle/Ellipse

In article <90F5CED3Cmmeijerixs4allnl_at_194.109.6.74>, Martijn Meijering says...
>
>mikharakiri_at_yahoo.com (Mikito Harakiri) wrote in
><bdf69bdf.0108060847.180f6d7c_at_posting.google.com>:
>>Do you mean that if we consider integers/reals as a plain set, monoid
>>or group, then integer is a subclass of reals, and if view them as a
>>field or a real vector space, then reals are a subclass of integers?
>
>Not quite: as a plain set, monoid or group the integers are indeed a
>subtype of the reals, as a field or vector space they are not, nor are the
>reals a subtype of the integers.

OK.

>Going from plain subset to real vector
>space, the subtype definitions get stronger. For example, if A is a
>*subfield* of B, that implies that A is a *subgroup* of B which implies
>that A is a *subset* of B. Therefore if the reals were a subfield of the
>integers they would have to be a subset as well and they're not.

I'm drawing parallels to Square/Rectangle and this still keeps me in confused state of mind. I have 2 specific questions:

1. {(1234), (3421), (2134), (4312)} is a subgroup of octic (dihedral) group. Yet, we want to subclass square (octic group) from rectangle (or {(1234), (3421), (2134), (4312)}.
2. The other way to express the same idea is to say that subclasses inherit symmetries of their ancestors. In that sence we vew subsetting on the set of symmetries, not the universe. Reals is simply more symmetrical class than integers. (Although, Mark is questioning practicality of such conclusion;-)

Would appreciate your input on those paradoxes (and you are also welcome to refer back to past discussion about state/transition diagramm interpretation). Received on Mon Aug 06 2001 - 13:57:21 CDT