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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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 JT Posts: 1,448 Registered: 4/7/12
Re: Outline: A Program to establish the continuity of points in a line
Posted: Feb 2, 2013 8:06 AM

On 2 Feb, 08:38, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 2, 2:21 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
> wrote:
>
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>

> > Decided to start a program.  An outline of my program follows.
>
> > Regards,
>
> > Ross Finlayson
>
> > A Program to establish the continuity of points in a line
>
> > The continuum of numbers is a primary feature of mathematics.   Logic
> > establishes structures modeling the numbers as abstract things.  Most
> > simple concepts of symmetry and conservation establish numerical
> > constructs and identities.  Points in a line are built from first and
> > philosophic principles of a logic, and a geometry of points and
> > space.  Their continuity is established.  Fundamental results of real
> > analysis are established on this line as of the continuum of real
> > numbers.  Identities are established for certain fundamental
> > properties of real numbers in a line in the geometry.

>
> > An axiomless system of natural deduction
> >         Conservation and symmetry in primary objects
> >         Categoricity of a general theory
> >                 Geometry
> >                 Number theory, analysis, and probability
> >                 Sets, partitions, types, and categories
> > A natural continuum from first principles
> >         The continuum in abstract
> >         A continuum of integers
> >         The establishment of a space of points from a continuum
> >         Drawing of a line in the space of points
> >         The polydimensional in space
> > Features of N
> >         The infinite in the natural continuum
> >         EF as CDF, the natural integers uniformly
> > Features of R
> >         Points as polydimensional
> >         Results in the polydimensional
> > Continuity in the real numbers
> >         Reductio of points in space
> >         Topological counterparts of the open and closed
> > Fundamental results of real analysis
> >         The complete ordered field in the space of points
> >         Fundamental theorems of integral calculus
> > Apologetics
> >         Infinitesimals and infinities
> >         Rational numbers and exhaustion
> >         The continuum as countable
> >                 Reflection on the drawing of the line as countable
> >                 Cantor's argument and counterexamples
> >                 A constructive interpretation of uncountable
> >         A retrofit of measure theory
> > Applications
> >         Applications in geometry
> >         Applications in probability
> >         Applications in physics

>
> fun random-walk()
>    r = rnd(4)
>    if (r=1)
>       x=x+1/10^y
>     if (r=2)
>      x=x-1/10^y
>    if (r=3)
>      y=y+1
>    if (r=4)&(y>1)
>      y=y-1
>    plot(x,y)
>
> fun infinite-walk()
>   x=0
>   y=1
>   repeat
>       random-walk()
>   until false
>
> Run this for an infinite amount of time and he walks over every point
> on the number line!
>
> PROOF:   no gaps!
>
> It's an infinite random walk with a twist.
> When he moves east or west, he covers 1 unit / 10^y units.
>
> 0---------1---------2---------3--->
>
> :) ------> :) ------> :)
>
> Here he is moving 1 unit positive at a time.
>
> When y increases - he takes 10 times smaller steps!
>
> 0---------1---------2---------3--->
>
> *----------*---------*-*
>
> y will reach every natural number
> and x will be every summation of every possible negative power of 10
> fraction!
>
> Herc
> --www.BLoCKPROLOG.com

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