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

MyWikiBiz, Author Your Legacy — Friday November 08, 2024
Jump to navigationJump to search
 
(4 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
==Majority Function Example==
+
__TOC__
 +
 
 +
==Majority Function Example 1.0==
 +
 
 +
===Proof 1 : Storyboard===
  
 
{| 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"
 
{| 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"
Line 40: Line 44:
 
|-
 
|-
 
| [[Image:Equational Inference QED.jpg|500px]]
 
| [[Image:Equational Inference QED.jpg|500px]]
 +
|}
 +
 +
===Proof 1 : Animation===
 +
 +
{| 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"
 +
|-
 +
| [[Image:Majority Function 600 x 300 Animation.gif]]
 +
|}
 +
 +
==Majority Function Example 2.0==
 +
 +
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].
 +
 +
{| align="center" cellpadding="10"
 +
|
 +
<math>\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}</math>
 +
|}
 +
 +
===Proof 1 : Storyboard===
 +
 +
{| 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"
 +
|-
 +
| [[Image:Majority Function Example Proof 1 Title.jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 1.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Reflect ab, ac, bc.jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 2.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Distribute (abc).jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 3.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Collect ab, ac, bc.jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 4.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Quit (a), (b), (c).jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 5.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Cancel (( )).jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 6.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Weed ab, ac, bc.jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 7.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Delete a, b, c.jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 8.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference Cancel (( )).jpg|500px]]
 +
|-
 +
| [[Image:Majority Function Example 2.0 Proof 1 Frame 9.jpg|500px]]
 +
|-
 +
| [[Image:Equational Inference QED.jpg|500px]]
 +
|}
 +
 +
===Proof 1 : Animation===
 +
 +
Here's an animated recap of the graphical transformations that occur in the above proof:
 +
 +
{| 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"
 +
|-
 +
| [[Image:Majority Function Example 2.0 Animation.gif]]
 
|}
 
|}

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
Retrieved from "https://mywikibiz.com/index.php?title=User:Jon_Awbrey/MOF&oldid=113659"