Lester Zick wrote: > On 19 Jul 2006 10:42:00 -0700, "MoeBlee" <email@example.com> wrote: > > >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. > > "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.
I am daunted just to behold your daring wordplay.
Are there any mathematical texts, particularly foundational ones, that your recommend?