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 8:06 AM


On 2 Feb, 08:38, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Feb 2, 2:21 pm, "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 > > fun randomwalk() > r = rnd(4) > if (r=1) > x=x+1/10^y > if (r=2) > x=x1/10^y > if (r=3) > y=y+1 > if (r=4)&(y>1) > y=y1 > plot(x,y) > > fun infinitewalk() > x=0 > y=1 > repeat > randomwalk() > until false > > 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. > > 0123> > > :) > :) > :) > > Here he is moving 1 unit positive at a time. > > When y increases  he takes 10 times smaller steps! > > 0123> > > **** > > y will reach every natural number > and x will be every summation of every possible negative power of 10 > fraction! > > Herc > www.BLoCKPROLOG.com
Why be a copy cat when you can be original http://www.youtube.com/watch?v=Dqm4dQv4F9w

