1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The Real-Line is a fractal

  1. Jun 8, 2004 #1
    ------------------------------------------------------------------------------------------------------
    "Real line" is used to mean real axis, i.e., a line with a fixed scale so that every real number corresponds to a unique point on the line. (http://mathworld.wolfram.com/RealLine.html)
    ------------------------------------------------------------------------------------------------------

    There are two basic states that stand in the basis of the real-line, which are:

    a) = (self identity).

    b) < or > (no self identity).


    Let x be a real number.

    Any real number, which is not x cannot be but < or > than x.

    The difference between x and not_x, defines a collection of infinitely many unique real numbers.

    The magnitude of this collection can be the same in any sub collection of it, which means that we have a structure of a fractal to the collection of the real numbers.

    In short, each real number exists in at least two states:

    a) As a member of R (local state).

    b) As an operator that defines the fractal level of R (a global operator on R).

    Any fractal has two basic properties, absolute and relative.


    The absolute property:

    Can be defined in any arbitrary level of the fractal, where within the level each real number has its unique "place" on the "real-line".


    The relative property:

    Any “sub R collection” in this case is actually R collection scaled by some R member as its global operator, and this is exactly the reason why some "sub R collections" can have the same magnitude as R collection.


    We can understand it better by this picture:

    http://www.geocities.com/complementarytheory/Real-Line.pdf


    In short, R collection has properties of a fractal.


    What do you think?
     
    Last edited: Jun 8, 2004
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: The Real-Line is a fractal
  1. Fractal or ? (Replies: 2)

  2. Fractals - Infinite? (Replies: 5)

Loading...