Date: Feb 1, 2013 11:21 PM
Subject: Outline: A Program to establish the continuity of points in a line

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