On 19 Jul 2006 16:22:52 -0700, "MoeBlee" <firstname.lastname@example.org> wrote:
>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.
More like childplay than wordplay when modern mathematikers have the unmitigated gall to co opt generic language terms the way they do and pretend no one will object then the unmitigated effrontery to insist that they know whereof they speak better than everyone else with straight faces.
>Are there any mathematical texts, particularly foundational ones, that >your recommend?
No idear. I've written a coupla basic tutorials covering specific issues mostly on the web. If you're really interested I can recommend some threads on the usenet going back to 2004.
Look, Moe, if someone tells me that "every point on a circle is equidistant from some point" I'm inclined to say thanks for the insight but I coulda probably figured that out for myself. But if someone comes along and tries to tell me "all points equidistant from any point is a circle" the way Bob Kolker did a year or so ago I'm inclined to say horseshit: you don't know what you're talking about. Then if someone comes along and tells me "I was really describing points on a plane" the way Bob tried to justify his definition then I'm inclined to say well that's true enough but you're citing facts not in evidence because you haven't defined a plane in comparable terms; you've just assumed everyone knows what you mean from Euclidean geometry not set theory.
Then if someone comes along and tells me that transcendentals are irrational and rationals and irrationals fall on one magic real number line I'm inclined to say someone has been receiving money for studying mathematics when all that's being studied is common fraud.