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#### Doron Shadmi

##### Guest

Hallo Dear people !

In the attached web site there is a short Email exchange, describing the foundations of a new theory of numbers.

http://www.geocities.com/complementarytheory/CATpage.html

I'll be glad to get your remarks and insights.

A quick reference of my acronyms:

---------------------------------

CAT = Complementary Associations Theory.

CD = Continuum XOR Discreteness (CAT's opposite concepts).

Association = Any possible mutual influence between opposite concepts

(under CAT its between Continuum and Discreteness).

EP = Explorable Product (exists iff it is an Association between CD).

AL = Association Level is an invariant quantity, being kept through

CD Associations.

CR = Computational Root is EP in AL.

RU = Redundancy and Uncertainty concepts, are used as invariant

structural degree of CR, determining its exact position in AL.

FRU = Full RU is the first CR in AL.

~RU = Not RU is the last CR in AL.

PRU = Partial RU is any CR which is not FRU and not ~RU.

FIS = Fractalic Information Structure, used to represent numbers

which are based on CRs.

NAB = Natural Axiom's Base is any property in some theory, that have

elements which are inaccessible to the other proprties of the

theory.

Yours,

Doron

In the attached web site there is a short Email exchange, describing the foundations of a new theory of numbers.

http://www.geocities.com/complementarytheory/CATpage.html

I'll be glad to get your remarks and insights.

A quick reference of my acronyms:

---------------------------------

CAT = Complementary Associations Theory.

CD = Continuum XOR Discreteness (CAT's opposite concepts).

Association = Any possible mutual influence between opposite concepts

(under CAT its between Continuum and Discreteness).

EP = Explorable Product (exists iff it is an Association between CD).

AL = Association Level is an invariant quantity, being kept through

CD Associations.

CR = Computational Root is EP in AL.

RU = Redundancy and Uncertainty concepts, are used as invariant

structural degree of CR, determining its exact position in AL.

FRU = Full RU is the first CR in AL.

~RU = Not RU is the last CR in AL.

PRU = Partial RU is any CR which is not FRU and not ~RU.

FIS = Fractalic Information Structure, used to represent numbers

which are based on CRs.

NAB = Natural Axiom's Base is any property in some theory, that have

elements which are inaccessible to the other proprties of the

theory.

Yours,

Doron

**Special thanks to Hurkyl:**Dear Hurkyl !

Thank you very much for being pedantic .

I made very important changes in my article, and I'll be glad

to get your comments on it.

Some Graphics of my number system representation of ALs 1 to 7 ,

you can find here:

http://cyborg2000.xpert.com/ctheory/ [Broken]

It is written in java by a friend of mine, and it is based on

Cartesian Product so, there are some left-right permutations

that can be ignored.

Thank you for your patience.

Yours,

Doron.

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