JT
Posts:
570
Registered:
4/7/12
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Re: Outline: A Program to establish the continuity of points in a line
Posted:
Feb 2, 2013 8:06 AM
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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:
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> > 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 random-walk()
> r = rnd(4)
> if (r=1)
> x=x+1/10^y
> if (r=2)
> x=x-1/10^y
> if (r=3)
> y=y+1
> if (r=4)&(y>1)
> y=y-1
> plot(x,y)
>
> fun infinite-walk()
> x=0
> y=1
> repeat
> random-walk()
> 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.
>
> 0---------1---------2---------3--->
>
> :) ------> :) ------> :)
>
> Here he is moving 1 unit positive at a time.
>
> When y increases - he takes 10 times smaller steps!
>
> 0---------1---------2---------3--->
>
> *----------*---------*-*
>
> 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
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