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

Let

Any real number, which is not

The difference between

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

Any fractal has two basic properties, absolute and relative.

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".

Any “sub

We can understand it better by this picture:

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

In short,

What do you think?

**"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

*be a real number.***x**Any real number, which is not

*cannot be but < or > than***x***.***x**The difference between

*and not_***x***, defines a collection of infinitely many unique real numbers.***x**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?

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