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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: 1,434 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:
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> > 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 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!
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> > 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 originalhttp://www.youtube.com/watch?v=Dqm4dQv4F9w

This is the way do be original