On Saturday, June 15, 2013 12:05:58 PM UTC-7, FredJeffries wrote: > On Jun 15, 9:12 am, "Ross A. Finlayson" <ross.finlay...@gmail.com> > > wrote: > > > > > > To refine to define the finite and non-finite, or infinite and non-infinite, usually non-finity is as shown with a set of ordinals that is Dedekind-finite or otherwise an unchanging amount of ordinals that is of to no limit ordinals, in infinite and transfinite ordinals. Defining infinity as change then non-infinity as dividing or divisible is so back to the non-infinite divides to itself, the infinite is only as to the related. > > > > > > So, counting or division could be read first in forward inference: for defining the non-finite by the counted finite, or the infinite by the non-infinite divided continuum (here with the continuum as infinite). > > > > > > This is plainly constructible, in terms of that the infinite (-ies) establish related rates of change as to the continuum. > > > > > > Then where the coordinates as it were are counted outward or to the origin, for the nilpotent and as in to partial products and transformation, they at once establish in one the other, in bounds then space. > > > > To feed your appetite for faux-post-modern gibberish,here is Jeanne > > Chervonna's "A Marxist-Jamesian Approach to the Axiom of Choice": > > https://bearspace.baylor.edu/Alexander_Pruss/www/HOAX.pdf
It's not irrelevant to your setup of topological concerns vis-a-vis set-theoretic concerns, features in topology of the continuum here of real numbers.
Then, generally I can see how one might consider mathematical developments from axiomless theory as absurd, circular, or dada, but as of the roots of endeavor in reason, it is well known that paradox (counterexample, from formal statement) and its explanation and resolution is a framework for the development of mathematical tools, for example Zeno, vis-a-vis the (convergent) limit as sum, as of fact.
Then, for noting features of the geometry and topology about R and R^n, real vector spaces, the polydimensional construction of points is of their construction as elements of the space, as the space is of them.
Then here in terms of the 1-, 4-, and 9-intersections of R^1, R^2, R^3, and working toward uniformity of points in density and regularity of points in distribution, here the polydimensional then is as to the points that define the lines and shapes, for the shapes that define lines that define points.
Then, here for N.P.s introduction of n^2-intersections in R^n as to being points, and of constructing region in R^n bounded by these things, here it was a simple note that of the points and intersections, there are some noted features for the 1-D case that would well extend into R^n, here at less than n^2, and one can consider a framework for translation between these resuls.
And for Fred Jeffries work in the regular in distributions: those features are only noted as being salient, and here, furthermore: ripe.
So, that is just an idea: features of the continuum in the polydimensional as to working in counterexamples in analysis. And: whether the naturals are compact in their infinitude, and the following workup of definitions of finity and infinity for each other, is a serious question, for mathematics. Because: for the Platonist: they are those things.
Then, how does mathematics digest itself? Here it is as to the Ouroboros as lemniscate, simply descriptively, with the acknowledgment that that's all it is.