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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 02:35, 14 August 2009
, 02:35, 14 August 2009→Outline Format
</ol>
</ol>
==Outline Format==
==Outline Formats==
<br>
{| align="center" cellpadding="8" width="90%"
{| align="center" cellpadding="8" width="90%"
\end{array}</math>
\end{array}</math>
|}
|}
<br>
{| align="center" cellpadding="4" width="90%"
| <big>•</big>
| colspan="3" | '''Transitive Law''' (Implicational Inference)
|-
| width="1%" |
| width="1%" |
| colspan="2" |
<math>\begin{array}{l}
~ p \le q
\\
~ q \le r
\\
\overline{~~~~~~~~~~~~~~~}
\\
~ p \le r
\end{array}</math>
|-
| valign="top" | <big>•</big>
| colspan="3" | By itself, the information <math>p \le q</math> would reduce our uncertainty from <math>\log 8\!</math> bits to <math>\log 6\!</math> bits.
|-
| valign="top" | <big>•</big>
| colspan="3" | By itself, the information <math>q \le r</math> would reduce our uncertainty from <math>\log 8\!</math> bits to <math>\log 6\!</math> bits.
|-
| valign="top" | <big>•</big>
| colspan="3" | By itself, the information <math>p \le r</math> would reduce our uncertainty from <math>\log 8\!</math> bits to <math>\log 6\!</math> bits.
|}
<br>
{| align="center" cellpadding="4" width="90%"
| <big>•</big>
| colspan="3" | '''Transitive Law''' (Equational Inference)
|-
| width="1%" |
| width="1%" |
| colspan="2" |
<math>\begin{array}{l}
~ p \le q
\\
~ q \le r
\\
=\!=\!=\!=\!=\!=\!=\!=
\\
~ p \le q \le r
\end{array}</math>
|-
| valign="top" | <big>•</big>
| colspan="3" | The contents and the measures of information that are associated with the propositions <math>p \le q</math> and <math>q \le r</math> are the same as before.
|-
| valign="top" | <big>•</big>
| colspan="3" | On its own, the information <math>p \le q \le r</math> would reduce our uncertainty from log(8) = 3 bits to log(4) = 2 bits, a reduction of 1 bit.
|}
<br>
==Mathematical Symbols==
==Mathematical Symbols==