Difference between revisions of "User:Jon Awbrey/MOF"

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==Majority Function Example==
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__TOC__
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==Majority Function Example 1.0==
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===Proof 1 : Storyboard===
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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|-
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| [[Image:Majority Function Example Proof 1 Title.jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 1.jpg|500px]]
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|-
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| [[Image:Equational Inference Reflect ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 2.jpg|500px]]
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|-
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| [[Image:Equational Inference Distribute (abc).jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 3.jpg|500px]]
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|-
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| [[Image:Equational Inference Collect ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 4.jpg|500px]]
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|-
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| [[Image:Equational Inference Quit (a), (b), (c).jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 5.jpg|500px]]
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|-
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 6.jpg|500px]]
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|-
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| [[Image:Equational Inference Weed ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 7.jpg|500px]]
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|-
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| [[Image:Equational Inference Delete a, b, c.jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 8.jpg|500px]]
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|-
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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|-
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| [[Image:Majority Function Example Proof 1 Frame 9.jpg|500px]]
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|-
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| [[Image:Equational Inference QED.jpg|500px]]
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|}
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===Proof 1 : Animation===
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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|-
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| [[Image:Majority Function 600 x 300 Animation.gif]]
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|}
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==Majority Function Example 2.0==
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Consider the following equation in boolean algebra, posted as a [http://mathoverflow.net/questions/9292/newbie-boolean-algebra-question problem for proof] at [http://mathoverflow.net/ MathOverFlow].
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{| align="center" cellpadding="10"
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|
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<math>\begin{matrix}
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a b \bar{c} + a \bar{b} c + \bar{a} b c + a b c
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\\[6pt]
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\iff
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\\[6pt]
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a b + a c + b c
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\end{matrix}</math>
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|}
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===Proof 1 : Storyboard===
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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|-
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| [[Image:Majority Function Example Proof 1 Title.jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 1.jpg|500px]]
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|-
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| [[Image:Equational Inference Reflect ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 2.jpg|500px]]
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|-
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| [[Image:Equational Inference Distribute (abc).jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 3.jpg|500px]]
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|-
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| [[Image:Equational Inference Collect ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 4.jpg|500px]]
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|-
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| [[Image:Equational Inference Quit (a), (b), (c).jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 5.jpg|500px]]
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|-
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 6.jpg|500px]]
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|-
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| [[Image:Equational Inference Weed ab, ac, bc.jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 7.jpg|500px]]
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|-
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| [[Image:Equational Inference Delete a, b, c.jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 8.jpg|500px]]
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|-
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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|-
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 9.jpg|500px]]
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|-
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| [[Image:Equational Inference QED.jpg|500px]]
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|}
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===Proof 1 : Animation===
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Here's an animated recap of the graphical transformations that occur in the above proof:
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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|-
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| [[Image:Majority Function Example 2.0 Animation.gif]]
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|}

Latest revision as of 02:30, 18 March 2010

Majority Function Example 1.0

Proof 1 : Storyboard

Majority Function Example Proof 1 Title.jpg
Majority Function Example Proof 1 Frame 1.jpg
Equational Inference Reflect ab, ac, bc.jpg
Majority Function Example Proof 1 Frame 2.jpg
Equational Inference Distribute (abc).jpg
Majority Function Example Proof 1 Frame 3.jpg
Equational Inference Collect ab, ac, bc.jpg
Majority Function Example Proof 1 Frame 4.jpg
Equational Inference Quit (a), (b), (c).jpg
Majority Function Example Proof 1 Frame 5.jpg
Equational Inference Cancel (( )).jpg
Majority Function Example Proof 1 Frame 6.jpg
Equational Inference Weed ab, ac, bc.jpg
Majority Function Example Proof 1 Frame 7.jpg
Equational Inference Delete a, b, c.jpg
Majority Function Example Proof 1 Frame 8.jpg
Equational Inference Cancel (( )).jpg
Majority Function Example Proof 1 Frame 9.jpg
Equational Inference QED.jpg

Proof 1 : Animation

Majority Function 600 x 300 Animation.gif

Majority Function Example 2.0

Consider the following equation in boolean algebra, posted as a problem for proof at MathOverFlow.

\(\begin{matrix} a b \bar{c} + a \bar{b} c + \bar{a} b c + a b c \\[6pt] \iff \\[6pt] a b + a c + b c \end{matrix}\)

Proof 1 : Storyboard

Majority Function Example Proof 1 Title.jpg
Majority Function Example 2.0 Proof 1 Frame 1.jpg
Equational Inference Reflect ab, ac, bc.jpg
Majority Function Example 2.0 Proof 1 Frame 2.jpg
Equational Inference Distribute (abc).jpg
Majority Function Example 2.0 Proof 1 Frame 3.jpg
Equational Inference Collect ab, ac, bc.jpg
Majority Function Example 2.0 Proof 1 Frame 4.jpg
Equational Inference Quit (a), (b), (c).jpg
Majority Function Example 2.0 Proof 1 Frame 5.jpg
Equational Inference Cancel (( )).jpg
Majority Function Example 2.0 Proof 1 Frame 6.jpg
Equational Inference Weed ab, ac, bc.jpg
Majority Function Example 2.0 Proof 1 Frame 7.jpg
Equational Inference Delete a, b, c.jpg
Majority Function Example 2.0 Proof 1 Frame 8.jpg
Equational Inference Cancel (( )).jpg
Majority Function Example 2.0 Proof 1 Frame 9.jpg
Equational Inference QED.jpg

Proof 1 : Animation

Here's an animated recap of the graphical transformations that occur in the above proof:

Majority Function Example 2.0 Animation.gif
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