Lester Zick wrote: > On 18 Jul 2006 11:42:33 -0700, "MoeBlee" <firstname.lastname@example.org> wrote: > > >MoeBlee wrote: > >> As I defined a 'circle', it is a set of points in RXR all > >> equidistant (for a distance greater than 0) from a given point. That's > >> a circle, not a sphere. > > > >I'm correcting myself. What I defined in RXR is both a circle and a > >sphere. For dimension greater than 2, such a set is not a circle but is > >a sphere. But it is not a disc nor a ball. > > No idea what this is in aid of. If you assume a plane you define a > circle? I agree. The difficulty is in set definitions you assume what > you should be demonstrating.
No, we don't. The definitions satisfy the criteria of eliminability and non-creatitivity. Also, RXR is proven to exist from the axioms and it is not even required to prove that RXR exists just to define the predicate 'is a circle'.