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I am almost ashamed to admit it but some of my best ideas come from the Recycle Bin or Trash Mathematics
Where Every - Any - Some - None serve as logical operators on Systems modeled with Numerical Functions. The Description breakdown follows in the table below: This Transformation gives functionality for any system
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Transformation component |
Operand / Example * |
Logical Operator |
Fruit Function Example * |
|
Every(x) |
Xc |
Uni |
Apple Fruit |
|
*/ |
|||
|
Any(x) |
Cx |
And (+) |
Apple + Orange + Pear |
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*/ |
|||
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Some(x) |
(Xc Cx) |
Uni and(+) Not(!) |
Apple Fruit ( Apple + Orange
+ Pear) |
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*/ |
|||
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None(x) |
(Xc Cx + !Xc Cx ) |
Not(!) |
! (Apple Fruit ( Apple + Orange
+ Pear) |
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Note: Numeric Negative is a loss of information and is not "Logical"
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Also the following illustrates the possible Sub Function Math Constructs of this System Transformation: