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Axiom
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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. |
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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 |
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..........or something like the above
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Expression of Sub System and Non Sub System give
highest degree of order? Expression of System and Non System gives
least degree of
order? Explaining Bible expression the Least is the Greatest and
Greatest is the least. Analysis of Nature of Expressions of Items
and/or Events and their Non Items and/or Events would be useful. ie
When/where do
these expressions occur and subsequent implications.....Note:
The observation that systems appear to produce but always quit after
a time.. Life Systems, and all other systems. Is there a Reason
for this?.....The expression of a Sub System and some System Ax
might be a Transformation combination giving a Transformation
category that would produce result of highest degree of order and
should be included in the above Transformation category table.
Birth of Numbers by Transformation Combinations of Principle System:.....: Expression of components of principal system by various combinations. For example: Top of Page
Why a Number Line exists
Every(A) ×/ Any(A)=1 unit 1,
Every(A) × (Any(A) + Any(A) ) = 2unit 1
Every(A) × (Any(A) + Any(A) + Any(A) ) = 3 unit 1
Every(A) ×/ (Any(A) / (Any(A) + Any(A))) = 1unit 1 / 2 unit 1......Rational , Real Number Line? TO Be continued
Missing Components , Some A and Non A , give full 'functionality' or relationships of the Number Line.
Expressions of Logic (+, - , /, × ) Logic , where Logic could be characterized as a form of Network, may be said to consist of another Network or Logic that was also Expressed by a form of Network or Logic........Work in Progress.
In the New Testament of the Bible, it says
there are repercussions for calling people fools.
Here is an expression documenting this result:
Non (Person A) + Non (Person B) + Non (Person C) = f
(D);
An expression of pure Non Functional Components
of People gives some unknown but functional result. This is per
the Math. Expression Constant Principle and the modeling of all
objects as Systems and their general system components.
| 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, Orange, Grape | f(x) | Apple + Non Apple + Orange + Non Orange + Grape + Non Grape |
| Life or Body system environment | Life or Body system functional capacity | DNA | non stated functionality , stupidity constant |
| 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. |
Author/Owner - Zim Olson Top of Page