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>
> Decided to start a program. An outline of my program follows.
> 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
> 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
> 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 in geometry
> Applications in probability
> Applications in physics
r = rnd(4)
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.
:) ------> :) ------> :)
Here he is moving 1 unit positive at a time.
When y increases - he takes 10 times smaller steps!
y will reach every natural number
and x will be every summation of every possible negative power of 10