```Date: Feb 2, 2013 2:38 AM
Author: Graham Cooper
Subject: Re: Outline: A Program to establish the continuity of points in a line

On Feb 2, 2:21 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>wrote:> 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 physicsfun 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 falseRun this for an infinite amount of time and he walks over every pointon 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 numberand x will be every summation of every possible negative power of 10fraction!Herc--www.BLoCKPROLOG.com
```