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 8:10 AM


On 2 Feb, 14:06, JT <jonas.thornv...@gmail.com> wrote: > 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 originalhttp://www.youtube.com/watch?v=Dqm4dQv4F9w
This is the way do be original http://www.youtube.com/watch?v=AaEmCFiNqP0

