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Directory talk:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 19:40, 9 July 2008
, 19:40, 9 July 2008→Original Format: HTML → TeX
====Original Format====
====Original Format====
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
|+ '''Table 5. A Bridge Over Troubled Waters'''
|+ '''Table 5. A Bridge Over Troubled Waters'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
|
|
<math>\begin{matrix}
<math>\begin{matrix}
\mathcal{X} & = &
\mathcal{X} & = & \{x_1, \ldots, x_n\} \\
\{x_1, \ldots, x_n\} \\
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
\underline\mathcal{X} & = &
\underline\mathcal{X} & = & \{\underline{x}_1, \ldots, \underline{x}_n\} \\
\{\underline{x}_1, \ldots, \underline{x}_n\} \\
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
\mathcal{A} & = &
\mathcal{A} & = & \{a_1, \ldots, a_n\} \\
\{a_1, \ldots, a_n\} \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{matrix}
X_i & = &
X_i & = & \langle x_i \rangle \\
\langle x_i \rangle \cong \mathbb{K} \\
& \cong & \mathbb{K} \\
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
\underline{X}_i & = &
\underline{X}_i & = & \{(\underline{x}_i), \underline{x}_i \} \\
\{(\underline{x}_i), \underline{x}_i \} \cong \mathbb{B} \\
& \cong & \mathbb{B} \\
\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
A_i & = &
A_i & = & \{(a_i), a_i \} \\
\{(a_i), a_i \} \cong \mathbb{B} \\
& \cong & \mathbb{B} \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
|
|
<math>\begin{matrix}
X & = & \langle \mathcal{X} \rangle \\
& = & \langle x_1, \ldots, x_n \rangle \\
& = & X_1 \times \ldots \times X_n \\
& = & \prod_{i=1}^n X_i \\
∏<sub>''i''</sub> ''X''<sub>''i''</sub><br>
& \cong & \mathbb{K}^n \\
\end{matrix}</math>
|
|
<u>''X''</u><br>
<math>\begin{matrix}
\underline{X} & = & \langle \underline\mathcal{X} \rangle \\
& = & \langle \underline{x}_1, \ldots, \underline{x}_n \rangle \\
{‹<u>''x''</u><sub>1</sub>, …, <u>''x''</u><sub>''n''</sub>›}<br>
& = & \underline{X}_1 \times \ldots \times \underline{X}_n \\
& = & \prod_{i=1}^n \underline{X}_i \\
∏<sub>''i''</sub> <u>''X''</u><sub>''i''</sub><br>
& \cong & \mathbb{B}^n \\
\end{matrix}</math>
|
|
<math>\begin{matrix}
A & = & \langle \mathcal{A} \rangle \\
& = & \langle a_1, \ldots, a_n \rangle \\
& = & A_1 \times \ldots \times A_n \\
& = & \prod_{i=1}^n A_i \\
∏<sub>''i''</sub> ''A''<sub>''i''</sub><br>
& \cong & \mathbb{B}^n \\
\end{matrix}</math>
|-
|-
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