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__General Information Framework (GIF) set theory__Set (which notated by "{" and "}") is an object that used as General Information Framework.

Set's property depends on its information's type.

There are 2 basic types of information that can be examined through GIF.

1.a) Empty set ={}

2.a) Non-empty set

(2.a) has 3 non-empty set's types:

1.b) Finitely many objects ( {a,b} ).

2.b) Infinitely many objects ( {a,b,...} ).

3.b) Infinite object ( {__} ).

(3.b) Is the opposite of the Empty set, therefore {__}=Full set.

__GIF has two limits:__

The lowest limit is {}(=Empty set).

The highest limit is {__}(=Full set).

Both limits are unreachable by (1.b) or (2.b) non-empty set's types.

Or in another words:

**Any information system exists in the open interval of ({},{__}).**

Infinitely many objects ( {a,b,...} ) cannot be completed, therefore words like 'all' or 'complete' cannot be used with sets that have infinitely many objects.

{} or {__} are actual infinity.

{a,b,...} is potential infinity.

An example:

http://www.geocities.com/complementarytheory/LIM.pdf

Question:

So what can we do with this theory that we can't do with standard set theory?

A non-formal answer (yet):

Please look at this two articles:

http://www.geocities.com/complementarytheory/ET.pdf

http://www.geocities.com/complementarytheory/CATheory.pdf

At this stage you have to look at them as non-formal overviews, but with a little help from my friends, they are going to be addressed in a rigorous formal way.

All the energy that was used to research the transfinite universes, is going to be used to research the information concept itself, including researches that explore our own cognition's abilities to create and develop the Math language itself.

By GIF set theory our models does not have to be quantified before we can deal with them, because GIF set theory has the ability to deal with any information structure in a direct way, which keeps its dynamic natural complexity during the research.

Concepts like symmetry-degree, Information's clarity-degree, uncertainty, redundancy and complementarity, are some of the fundamentals of this theory.

Organic

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