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User:Jon Awbrey/Figures and Tables 16

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Logical Graphs 3.0

Axioms

The axioms are just four in number, divided into the arithmetic initials, and and the algebraic initials, and

Axiom I1.png
Axiom I2.png
Axiom J1.png
Axiom J2.png

Double Negation • Theorem

Double Negation 3.0.png

Double Negation • Proof

Double Negation Proof 3.0.png

Double Negation • Animation

The steps of this proof are replayed in the following animation.

Double Negation 2.0 Animation.gif

Double Negation • Components

The proof that follows is adapted from the one that was given by George Spencer Brown in his book Laws of Form (LOF) and credited to two of his students, John Dawes and D.A. Utting.

Double Negation 1.0 Marquee Title.png
Double Negation 1.0 Storyboard 1.png
Equational Inference I2 Elicit (( )).png
Double Negation 1.0 Storyboard 2.png
Equational Inference J1 Insert (a).png
Double Negation 1.0 Storyboard 3.png
Equational Inference J2 Distribute ((a)).png
Double Negation 1.0 Storyboard 4.png
Equational Inference J1 Delete (a).png
Double Negation 1.0 Storyboard 5.png
Equational Inference J1 Insert a.png
Double Negation 1.0 Storyboard 6.png
Equational Inference J2 Collect a.png
Double Negation 1.0 Storyboard 7.png
Equational Inference J1 Delete ((a)).png
Double Negation 1.0 Storyboard 8.png
Equational Inference I2 Cancel (( )).png
Double Negation 1.0 Storyboard 9.png
Equational Inference Marquee QED.png