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Topic: Outline: A Program to establish the continuity of points in a line
Replies: 15   Last Post: Feb 15, 2013 5:58 PM

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 JT Posts: 1,448 Registered: 4/7/12
Re: Outline: A Program to establish the continuity of points in a line
Posted: Feb 2, 2013 8:00 AM

On 2 Feb, 05:21, "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

Oh another copy cat, maybe you did not pass anal exams.