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Topic: Outline: A Program to establish the continuity of points in a line
Replies: 15   Last Post: Feb 15, 2013 5:58 PM

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 ross.finlayson@gmail.com Posts: 2,713 Registered: 2/15/09
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 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 points
2) area bounded by integer lattice points (here 4-many, the unit
square)
3) rationals (here 1/2 particularly for symmetrical complements, then
generally)
4) the triangle (or rather tri-lateral) halving the unit square via
symmetry
5) its area then generally

This has unit hyper-volume of the unit n-cube.

Fred, the area of the triangle is determined by its sides.

Regards,

Ross Finlayson