
Re: Outline: A Program to establish the continuity of points in a line
Posted:
Feb 1, 2013 11:37 PM


On Fri, 1 Feb 2013, Ross A. Finlayson wrote:
> Decided to start a program. An outline of my program follows. > > 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
What does that last line all mean?
> 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 >

