```Date: Feb 2, 2013 5:47 PM
Author: ross.finlayson@gmail.com
Subject: Re: Outline: A Program to establish the continuity of points in a line

On Feb 2, 1:22 pm, FredJeffries <fredjeffr...@gmail.com> wrote:> On Feb 2, 1:02 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>> wrote:>>>> > It might be remiss to not note that of course there are a wide variety> > of mathematical developments over time and in history that don't> > necessarily have as much approbation as they should in the> > contemporary, with Cauchy/Dedekind/Weierstrass in analysis then to> > Cantor, Russell, and Zermelo and Fraenkel in axiomatic foundations as> > "modern".  Newton's, Leibniz', and du Bois-Reymond's infinitesimals> > are notably absent from the one (though Leibniz' notation survives),> > and primary notions of Kant, Hegel, Frege, Quine, Popper the other.> > As well, there are modern attempts to formulate these particular> > notions of the integers as infinite and reals as complete that aren't> > the standard, in light of and in extension of the standard, for> > example of Aczel, Priest, Boucher, Paris and Kirby, and Bishop and> > Cheng.>> There is one outstanding difference between all of those and the> gibberish you post: All of them can be used to solve actual problems> whereas you still cannot show how to use your nonsense to do even> something as simple as determining the area of a triangle.This could be done in this program in this manner, establishing:1) the integer lattice points2) area bounded by integer lattice points (here 4-many, the unitsquare)3) rationals (here 1/2 particularly for symmetrical complements, thengenerally)4) the triangle (or rather tri-lateral) halving the unit square viasymmetry5) its area then generallyThis has unit hyper-volume of the unit n-cube.Fred, the area of the triangle is determined by its sides.Regards,Ross Finlayson
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