II.   Divine Systems

The PRIMARY RULES of the ELEMENTAL CONCEPT of UNISET of the UNISET FOUNDATION CLASS of the EIKOS Language System are:

1. UNISET is a FOUNDATION CLASS of ELEMENTAL CONCEPTS associated with the study of all principles and rules of definition by which SETS are defined, classified and used in valid statements defined by the EIKOS Language System.

2. UNISET is constructed of sixteen [16] ELEMENTAL CONCEPTS including: UNISET, SET, MEMBER, INFINITY, INHERITANCE, DEPENDENCY, SPECIALIZATION, FOUNDATION SET, FOUNDATION STATE SET, FOUNDATION MOTION SET, FINITE SET SERIES, INFINITE SET SERIES, NATURAL SET SERIES, THEORETICAL SET SERIES, SET LOGOS and SET LOGIC.

3. All CONCEPTS, OBJECTS and NUMBERS are a SET of UNISET.

4. All CONCEPTS, OBJECTS and NUMBERS may be described as a FRACTION of the SET of 0 to 1 to some exponential POWER.

5. 0 is a MEMBER of 1 and itself.

6. 1 is a SET and a MEMBER of itself.

7. The SUM of these PROPERTIES is known as the UNISET.

8. If one MEMBER of the UNISET ceased to exist, the total set being UNISET would cease to exist.

9. The existence of UNISET is therefore dependent on the EXISTENCE of each individual MEMBER of the SET for itself to exist.

The PRIMARY RULES of the ELEMENTAL CONCEPT of INFINITY of the UNISET FOUNDATION CLASS of the EIKOS Language System are:

1. INFINITY is both a unique NUMBER and a SET.

2. INFINITY equals the UNISET less 1.

3. All NUMBERS may be described by the NUMBER INFINITY.

4. All NUMBERS may be described in SETS of degrees of INFINITY.

5. As EXISTENCE depends upon INFINITY + 1, the NUMBER continues to grow at a predictable RATE.

6. INFINITY is the BOUNDARY NUMBER of all REAL NUMBERS. Only the imaginary number of UNISET is greater.

The PRIMARY RULES of the ELEMENTAL CONCEPT of INHERITANCE of the UNISET FOUNDATION CLASS of the EIKOS Language System are:

1. A MEMBER of a SET INHERITS the PROPERTIES of the SET to which it belongs.

2. All OBJECTS of a SET share common PROPERTIES to some degree according to their INHERITANCE of SETS.

3. All OBJECTS of SETS have unique PROPERTIES to some degree according to their specialized INHERITANCE of SETS.

The PRIMARY RULES of the ELEMENTAL CONCEPT of FOUNDATION MOTION SET of the UNISET FOUNDATION CLASS of the EIKOS Language System are:

1. A FOUNDATION MOTION SET is any SET expressed by its DIMENSION and some kind of active MOTION of its ELEMENTS.

2. There are two (2) main kinds of FOUNDATION MOTION SETS, GROWTH and DECAY.

3. A SIMPLE GROWTH SET denotes the statement - "the sum SET of all elements of type [a] by ADDITION as the NUMBER of the SET [t] increases by 1 as the value of type [a] elements increase from value [x] to [z] by method [c]".

4. A SIMPLE EXPONENTIAL GROWTH SET denotes the statement - "the sum SET of all elementsof type [a] by MULTIPLICATION as the NUMBER of the SET [t] increases by 1 as the value of type [a] elements increase from value [x] to [z] by method [c]".

5. A SIMPLE DECAY SET denotes the statement - "the sum SET of all elements of type [a] by SUBTRACTION as the NUMBER of the SET [t] increases by 1 as the value of type [a] elements decrease from value [x] to [z] by method [c]".

6. A SIMPLE EXPONENTIAL DECAY SET denotes the statement - "the sum SET of allelements of type [a] by DIVISION as the NUMBER of the SET [t] increases by 1as the value of type [a] elements decrease from value [x] to [z] by method [c]".

7. The FOUNDATION MOTION SET SYMBOLS of the Eikos Language System are equivalent to the summation and product symbols used by mathematics. .