On 19 Jul 2006 10:42:00 -0700, "MoeBlee" <firstname.lastname@example.org> wrote:
>Lester Zick wrote: >> On 18 Jul 2006 11:42:33 -0700, "MoeBlee" <email@example.com> 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.
"Non creativity" is sure hell the truth since you have the hutzpah just to assume what you can't demonstrate.
> 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'.
It is certainly not required to baldly assert the predicate is a circle even though it's really a sphere. Just takes balls.
If such definitions satisfy criteria of non creativity and eliminability they should be non creatively eliminated.