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Zim Mathematics: Creative Axiom List
The purpose for this page is to show the availability of axioms other than those developed in the Applications section. Demonstrating that useful Axioms can be found that may seem to contradict already known Axioms, that are  useful and also self evident.   I hope to continually add material myself to this section.
System Algebra Love, Logic; Least, Greatest Paradox Number Line System Metaphors Math Objects Grammar Interpretations
  'Exhaustive'
Non-Functional
Expression List
Fool Expression Network Logic 'Exhaustive'
Expressions
of God
 



 

System - Sub System 'Algebra'

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Operations as Systems Unit Transformation Operations as Sub Systems Unit Transformation
System (+,-,*,/) Sub System

Sub System (+, -,*, /) Sub System

System (+, -,*, /) System
x


x


x
X or Constant (unique)

X


X or A
System (+, -,*, /) Sub System

Sub System (+, -,*, /) Sub
System

System (+, -,*, /) System

 

C


C


C
A


A or B or X


A or B or X
 
'System-Sub System Algebra, Transformation Categories of expressions of Systems - Sub Systems,  The following categories are derived from Constant unit unknown expressions I developed in 1984 and their various derivations.  At the time I developed these expressions, I just thought they were a neat way to characterize  Quantitative and Qualitative values. But they have proven useful in characterizing these System - Sub System expression  combinations. 

Examples of Systems and/or  Sub Systems are:  Apple Tree System, Apple B,  Apple Tree Branch A;  Apple A System and Orange B System,  Apple System and Apple Seed Sub System, Human Body System and  Human Body Organs Sub System(s), Universe System and Planetary Sub Systems; Apple System, Orange System, Apple Seed Sub System; Atomic-Molecular Systems and their  Sub Systems...A operational sub system could be operations within above mentioned systems.  A operational system would be external to mentioned systems
Operations in this breakdown are considered Systems.
Operations are Sub Systems in this breakdown and by default within the System A
System   A  ( / ,*)    System B;  Transformation X unit x System   A  (   /,* )    System B;  Transformation  A  unit constant   ?
System A    ( / ,*)    Sub System B  ; Normal Transformational or Factorial System A    ( / ,*)    Sub System B  ; Transformational  A unit constant
System A  ( / ,*)   System A ;  Transformation  X unit constant

System A  ( / ,*)   System A ; Transformation A unit constant

Sub System B  ( / ,*)   Sub System B  ;  Transformation X unit x. Sub System B  ( / ,*)   Sub System B  ;  Transformation X unit constant
Sub System A  ( / ,*)   Sub System B  ;  Transformation X unit x. Sub System A  ( / ,*)   Sub System B  ;  Transformation X unit constant
System   A  -    System B;  Non Transformational, Non Intelligent. or X unit x. System   A  -    System B;   Transformation  A unit constant
System   A  +    System B;  Non Transformational, Non Intelligent System   A  +    System B;  Transformation C unit x.
System A   -    Sub System B  ; Transformation X unit x System A   -    Sub System B  ; Transformation A unit constant
System A    +    Sub System B  ; Transformation C unit x System A    +    Sub System B  ; Transformation A unit constant
System A  -  System A =  Transformation XA unit x System A  -  System A =  Transformation A unit constant. 
System A + System A = Transformation XA unit x
System A + System A = Transformation A unit constant
Sub System B  -  Sub System B ; Transformation X unit x. Sub System B  -  Sub System B ; Transformation A unit constant
Sub System B + Sub System B ; Transformation X unit constant Sub System B + Sub System B ; Transformation A unit constant
Sub System B  -  Sub System A ; Transformation X unit x Sub System B  -  Sub System A ; Transformation A unit x; 
Sub System B + Sub System A ; Transformation X unit x  Sub System B + Sub System A ; Transformation A unit x
   
..........or something like the above

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Love, Logic and Order Expressions

                                        or

 

Apple/Fruit System Sub System


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 Network Logic

 

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Fool Expression

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Multiple Metaphors, Contexts and Meanings for the four General System Behavioral Components:
Every(x) Any(x) Some(x) Non(x)
 functional context,     traditional working matrix for Mathematics purpose, reason, actual function non functional  component, or non stated functionality
Every(+)Every(-)Every(*)Every(/) Any(+)Any(-)Any(*)Any(/) Some(+)Some(-)Some(*)Some(/) Non(+)Non(-)Non(*)Non(/)
functional context of Principal System complete set items/events of Universe functional intersection of:
functional context of Principal System,  complete set of Universe,  all knowledge
all knowledge
Fruit(x) Apple + Non Apple + Orange + Non Orange + Grape + Non Grape f(x) Non Apple +  Non Orange + Non Grape
Life or Body system environment Life or Body system functional capacity DNA non stated functionality , stupidity constant, mutations
Molecules, Scientist, etc. Atoms Quantum Theory non causal/effect
Constant unit unknown
(Symbol as example)
A-Z Intersection of other components - giving definition  domain. Visualizing components in Venn Diagram.  A-Z (+, - ,*, / )
Qualitative Unique Object(s) Intersection of other components functionality f(0) = + / - *
  f(1) = + - / *

1 variable - 1 Any ; + - / * ; basic operations expressed as systems.
  f(1 + 0) = + - / *

1 variable - 1 Any. 0 variable - 0 Any  . + - / * ; basic operations expressed as systems.  1 + 0 , the functionality of any object and it's non functionality.
  f(1, 0) = + - / *;
Intersection of other components functionality. Visualized in a Venn Diagram.

1 variable - 1 Any. 0 variable - 0 Any  ; + - / *; basic operations expressed as systems.
  f(0) = + - / *

0 variable - 0 Any  ;+ - / * ; basic operations expressed as systems.
       
       
       

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All Objects as Systems  and Operations as  Systems

All Objects in this portion are Sub Systems expressed as Systems of  a  Principal System. Operations are intended to be independent Systems as generally in Mathematics , but could be considered  as a sub system to some principal system.

 

 

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Zim Math Grammar Interpretations

A is  a Principal System; B, C are Sub Systems.

 

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'Exhaustive' List of Non-Functional Expressions

Non Functional Expressions could be said to consist of Partial System constructs or System Wide Expressions or both.  The nature of the expressed Non-Functional construct could be said to be: Numeric, Qualitative, an Unknown Construct or some combination of all these possibilities. Here is a small sampling of these possibilities:

 

The operations below denote either a complete system construct or partial system construct.

 

 

More Non-Functional Expressions below:

 

 

 

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Complete Survey of Expressions of God

An expression of God or an expression of an object with the full functional capacity offered by God could be said to consist of any  function (A-Z) or Numeric construct(s) or Unknown Construct(s) or some combination thereof of numeric objects 1 and/or 0  expressed with basic operations modeled as complete systems.  Here are some of the possible initial expression construct(s)

 

 

 

 

( "G_D" , could be considered a new form of Math Construct. It is neither a qualitative, numeric, or an unknown construct, putting this into its own category of  symbolic-Math construct.  I had experimented with other forms of such constructs in 1985, with math expressions of so called Chinese symbols (I know no Chinese) .)

 

 

 

Author/Owner - Zim Olson            Top of Page

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