
Re: Outline: A Program to establish the continuity of points in a line
Posted:
Feb 2, 2013 5:47 PM


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 BoisReymond'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 points 2) area bounded by integer lattice points (here 4many, the unit square) 3) rationals (here 1/2 particularly for symmetrical complements, then generally) 4) the triangle (or rather trilateral) halving the unit square via symmetry 5) its area then generally
This has unit hypervolume of the unit ncube.
Fred, the area of the triangle is determined by its sides.
Regards,
Ross Finlayson

