Real line is used to mean real axis

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"Real line" is used to mean real axis

["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 fractal properties.


What do you think?

 

[baffledMatt]

Sorry, what does any of this have to do with fractals?

Matt

 

[geistkiesel]

"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)

Let us think about a single point, which is corresponds to number 0.

Any real number which is not 0 cannot be but < or > than 0.

The name which we choose to give to another point which is not the point that mapped with number 0, define a mathematical universe of infinitely many unique numbers.

The magnitude of this universe is the same in any sub universe of it, which means that we have an internal structure of a fractal to the universe of the real numbers.


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:

Between any two arbitrary different scales there can be infinitely many levels where the relative proportion between them is being kept, and this is exactly the reason why any sub universe has the same magnitude.

We can understand it better by this picture:

http://www.geocities.com/complementarytheory/real-Model.jpg


I'll be glad to get your comments

Just an observation: Yiou picked 0 as < 0 > , but yu could pick any number and get the same result < 7 > , o even < pi > or any irrational number. I am asking, not tellin, do these onservations have any elling efect on whatyou wou were saying in your post?

Also, as a natura skeptic, I was born with the affliction, are you suggesting the subfractal world is a reflection of some kind of physical symmetry? In other words do the laws of physics apply as reflected in fractal theory? Recursion, per se, doesn't necessarily bother me.

 

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geistkiesel and baffledMatt,

I made a major update to my first post, please read it again and I'll be glad to get your remarks and insights.