In article <email@example.com>, Lester Zick <DontBother@nowhere.net> wrote:
> On Fri, 14 Jul 2006 18:41:42 -0300, "Shmuel (Seymour J.) Metz" > <firstname.lastname@example.org> wrote: > > >In <email@example.com>, on 07/13/2006 > > at 09:42 AM, firstname.lastname@example.org said: > > > >>However typical set theory definitions which run > >>along the lines of a "set of all points which . . ." do turn out to > >>be a joke because they invariably rely on various geometric > >>assumptions regarding figures such as planes, lines, etc. > > > >Nonsense. Set Theory neither relies on geometric assumptions nor does > >it talk about figures. Now, you can certainly apply Set Theory to > >Geometry, but then what you have are geometric definitions, not Set > >Theory definitions. > > Are you an idiot? If you define a circle as the "set of all points > equidistant from any point" you are not using a set theory definition > for a geometric figure?
As no set theory of my acquaintance requires any definition of distances between points, I would say that any definition which does refer to distances is certainly not purely set theoretic, and is at least partly geometric.