On 17 Jul 2006 22:29:00 -0700, firstname.lastname@example.org wrote:
>Lester Zick wrote: > >> It has often been stated to me as zero and suc(0). I don't agree that >> zero is a natural number but for what it's worth there it is. >> > >But surely you agree that 1 is the loneliest number?
Definitely. I'm not sure I'm the loneliest but pretty close to it.
>Although there are some who claim that 2 can be as bad as 1, it is >generally accepted [*] that 2 is the loneliest number /since/ the >number 1. It has also been more directly claimed that 1 is strictly >worse than 2, "whoah-oh" [ibid]. > ><snip> > >> Except this seems to define a sphere. > >In fact, a 1-sphere; also known as a circle.
I should have thought the 1 sphere would have been known as a straight line, the circle as a 2 sphere. My main problem seems to be there aren't any connections between n spheres and set theory. All I can see set theorists doing is assuming auxilliary geometric notions about whatever they want to pretend is defineded by set theory and then claiming they're defined by set theory when the most they can actually claim is that their various assumptions about geometric objects are vaguely described numerically by set theory.
> It's been conjectured to >be the loneliest n-sphere since the 0-sphere; although Nilsson et al >have yet to express an opinion on this.
Personally I find that 1 and suc(1) define 1, 2, e, 3, pi, 4 etc. I recognize this diverges from conventional assumptions but for what it's worth there it is.