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 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