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Revision as of 16:42, 7 July 2008
, 16:42, 7 July 2008→The Analogy Between Real and Boolean Types: HTML → TeX
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
|+ '''Table 3. Analogy of Real and Boolean Types'''
|+ '''Table 3. Analogy Between Real and Boolean Types'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
! <math>\mbox{Real Domain}\ \mathbb{R}</math>
! <math>\mbox{Real Domain}\ \mathbb{R}</math>
! <math>\mbox{Boolean Domain}\ \mathbb{B}</math>
! <math>\mbox{Boolean Domain}\ \mathbb{B}</math>
|-
|-
| <math>\mathbb{R}^n</math><sup>
| <math>\begin{smallmatrix}\mathbb{R}^n\end{smallmatrix}</math>
| <math>\mbox{Basic Space}\!</math>
| <math>\begin{smallmatrix}\mbox{Basic Space}\end{smallmatrix}</math>
| <math>\mathbb{B}^n</math><sup>
| <math>\begin{smallmatrix}\mathbb{B}^n\end{smallmatrix}</math>
|-
|-
| <math>\mathbb{R}^n \to \mathbb{R}</math>
| <math>\begin{smallmatrix}\mathbb{R}^n \to \mathbb{R}\end{smallmatrix}</math>
| <math>\mbox{Function Space}\!</math>
| <math>\begin{smallmatrix}\mbox{Function Space}\end{smallmatrix}</math>
| <math>\mathbb{B}^n \to \mathbb{B}</math>
| <math>\begin{smallmatrix}\mathbb{B}^n \to \mathbb{B}\end{smallmatrix}</math>
|-
|-
| <math>(\mathbb{R}^n \to \mathbb{R}) \to \mathbb{R}</math>
| <math>\begin{smallmatrix}(\mathbb{R}^n \to \mathbb{R}) \to \mathbb{R}\end{smallmatrix}</math>
| <math>\mbox{Tangent Vector}\!</math>
| <math>\begin{smallmatrix}\mbox{Tangent Vector}\end{smallmatrix}</math>
| <math>(\mathbb{B}^n \to \mathbb{B}) \to \mathbb{B}</math>
| <math>\begin{smallmatrix}(\mathbb{B}^n \to \mathbb{B}) \to \mathbb{B}\end{smallmatrix}</math>
|-
|-
| <math>\mathbb{R}^n \to ((\mathbb{R}^n \to \mathbb{R}) \to \mathbb{R})</math>
| <math>\begin{smallmatrix}\mathbb{R}^n \to ((\mathbb{R}^n \to \mathbb{R}) \to \mathbb{R})\end{smallmatrix}</math>
| <math>\mbox{Vector Field}\!</math>
| <math>\begin{smallmatrix}\mbox{Vector Field}\end{smallmatrix}</math>
| <math>\mathbb{B}^n \to ((\mathbb{B}^n \to \mathbb{B}) \to \mathbb{B})</math>
| <math>\begin{smallmatrix}\mathbb{B}^n \to ((\mathbb{B}^n \to \mathbb{B}) \to \mathbb{B})\end{smallmatrix}</math>
|-
|-
| <math>(\mathbb{R}^n \times (\mathbb{R}^n \to \mathbb{R})) \to \mathbb{R}</math>
| <math>\begin{smallmatrix}(\mathbb{R}^n \times (\mathbb{R}^n \to \mathbb{R})) \to \mathbb{R}\end{smallmatrix}</math>
| <font size="4">"</font>
| <font size="4">"</font>
| <math>(\mathbb{B}^n \times (\mathbb{B}^n \to \mathbb{B})) \to \mathbb{B}</math>
| <math>\begin{smallmatrix}(\mathbb{B}^n \times (\mathbb{B}^n \to \mathbb{B})) \to \mathbb{B}\end{smallmatrix}</math>
|-
|-
| <math>((\mathbb{R}^n \to \mathbb{R}) \times \mathbb{R}^n) \to \mathbb{R}</math>
| <math>\begin{smallmatrix}((\mathbb{R}^n \to \mathbb{R}) \times \mathbb{R}^n) \to \mathbb{R}\end{smallmatrix}</math>
| <font size="4">"</font>
| <font size="4">"</font>
| <math>((\mathbb{B}^n \to \mathbb{B}) \times \mathbb{B}^n) \to \mathbb{B}</math>
| <math>\begin{smallmatrix}((\mathbb{B}^n \to \mathbb{B}) \times \mathbb{B}^n) \to \mathbb{B}\end{smallmatrix}</math>
|-
|-
| <math>(\mathbb{R}^n \to \mathbb{R}) \to (\mathbb{R}^n \to \mathbb{R})</math>
| <math>\begin{smallmatrix}(\mathbb{R}^n \to \mathbb{R}) \to (\mathbb{R}^n \to \mathbb{R})\end{smallmatrix}</math>
| <math>\mbox{Derivation}\!</math>
| <math>\begin{smallmatrix}\mbox{Derivation}\end{smallmatrix}</math>
| <math>(\mathbb{B}^n \to \mathbb{B}) \to (\mathbb{B}^n \to \mathbb{B})</math>
| <math>\begin{smallmatrix}(\mathbb{B}^n \to \mathbb{B}) \to (\mathbb{B}^n \to \mathbb{B})\end{smallmatrix}</math>
|-
|-
| <math>\mathbb{R}^n \to \mathbb{R}^m</math>
| <math>\begin{smallmatrix}\mathbb{R}^n \to \mathbb{R}^m\end{smallmatrix}</math>
| <math>\mbox{Basic Transformation}\!</math>
| <math>\begin{smallmatrix}\mbox{Basic Transformation}\end{smallmatrix}</math>
| <math>\mathbb{B}^n \to \mathbb{B}^m</math>
| <math>\begin{smallmatrix}\mathbb{B}^n \to \mathbb{B}^m\end{smallmatrix}</math>
|-
|-
| <math>(\mathbb{R}^n \to \mathbb{R}) \to (\mathbb{R}^m \to \mathbb{R})</math>
| <math>\begin{smallmatrix}(\mathbb{R}^n \to \mathbb{R}) \to (\mathbb{R}^m \to \mathbb{R})\end{smallmatrix}</math>
| <math>\mbox{Function Transformation}\!</math>
| <math>\begin{smallmatrix}\mbox{Function Transformation}\end{smallmatrix}</math>
| <math>(\mathbb{B}^n \to \mathbb{B}) \to (\mathbb{B}^m \to \mathbb{B})</math>
| <math>\begin{smallmatrix}(\mathbb{B}^n \to \mathbb{B}) \to (\mathbb{B}^m \to \mathbb{B})\end{smallmatrix}</math>
|-
|-
| <math>\ldots\!</math>
| <math>\ldots\!</math>
