Date: Feb 1, 2013 11:21 PM
Author: ross.finlayson@gmail.com
Subject: Outline: A Program to establish the continuity of points in a line
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