- #1

#### Doron Shadmi

Hallo Dear people !

In the attached website 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 website 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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