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MyWikiBiz, Author Your Legacy — Wednesday October 15, 2025
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==Format Samples • Wiki Text==
===MathBB, MathBF, MathCal===
A set of logical features, <math>\mathcal{A} = \{ a_1, \ldots, a_n \},</math> affords a basis for generating an <math>n</math>-dimensional universe of discourse, written <math>A^\bullet = [ \mathcal{A} ] = [ a_1, \ldots, a_n ].</math> It is useful to consider a universe of discourse as a categorical object that incorporates both the set of points <math>A = \langle a_1, \ldots, a_n \rangle</math> and the set of propositions <math>A^\uparrow = \{ f : A \to \mathbb{B} \}</math> that are implicit with the ordinary picture of a venn diagram on <math>n</math> features. Accordingly, the universe of discourse <math>A^\bullet</math> may be regarded as an ordered pair <math>(A, A^\uparrow)</math> having the type <math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B})),</math> and this last type designation may be abbreviated as <math>\mathbb{B}^n\ +\!\to \mathbb{B},</math> or even more succinctly as <math>[ \mathbb{B}^n ].</math> For convenience, the data type of a finite set on <math>n</math> elements may be indicated by either one of the equivalent notations, <math>[n]</math> or <math>\mathbf{n}.</math>
===MathFrak===
<p><math>\begin{array}{lccccccccccc}
\mathfrak{M}
& = & \{ & \mathfrak{m}_1 & , & \mathfrak{m}_2 & , & \mathfrak{m}_3 & , & \mathfrak{m}_4 & \}
\\
& = & \{ & \text{“ ”} & , & \text{“(”} & , & \text{“,”} & , & \text{“)”} & \}
\\
& = & \{ & \mathrm{blank} & , & \mathrm{links} & , & \mathrm{comma} & , & \mathrm{right} & \}
\end{array}</math></p>
===TextTT===
For the initial case <math>k = 0,</math> the bound connective is an empty closure, an expression taking one of the forms <math>\texttt{()}, \texttt{( )}, \texttt{( )}, \ldots</math> with any number of spaces between the parentheses, all of which have the same denotation among propositions.
For the generic case <math>k > 0,</math> the bound connective takes the form <math>\texttt{(} s_1 \texttt{,} \ldots \texttt{,} s_k \texttt{)}.</math>
==Format Samples • Screenshots==
===MathJax Fail===
[[File:Format Samples • MathJax Fail.png|640px]]
===MathML View===
[[File:Format Samples • MathML View.png|640px]]
==Logic of Relatives==
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 3. Relational Composition
o---------o---------o---------o---------o
| # !1! | !1! | !1! |
o=========o=========o=========o=========o
| L # X | Y | |
o---------o---------o---------o---------o
| M # | Y | Z |
o---------o---------o---------o---------o
| L o M # X | | Z |
o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:60%"
|+ <math>\text{Table 3. Relational Composition}\!</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
|-
| style="border-right:1px solid black" | <math>L\!</math>
| <math>X\!</math>
| <math>Y\!</math>
|
|-
| style="border-right:1px solid black" | <math>M\!</math>
|
| <math>Y\!</math>
| <math>Z\!</math>
|-
| style="border-right:1px solid black" | <math>L \circ M</math>
| <math>X\!</math>
|
| <math>Z\!</math>
|}
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 9. Composite of Triadic and Dyadic Relations
o---------o---------o---------o---------o---------o
| # !1! | !1! | !1! | !1! |
o=========o=========o=========o=========o=========o
| G # T | U | | V |
o---------o---------o---------o---------o---------o
| L # | U | W | |
o---------o---------o---------o---------o---------o
| G o L # T | | W | V |
o---------o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:75%"
|+ <math>\text{Table 9. Composite of Triadic and Dyadic Relations}\!</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:20%" |
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
|-
| style="border-right:1px solid black" | <math>G\!</math>
| <math>T\!</math>
| <math>U\!</math>
|
| <math>V\!</math>
|-
| style="border-right:1px solid black" | <math>L\!</math>
|
| <math>U\!</math>
| <math>W\!</math>
|
|-
| style="border-right:1px solid black" | <math>G \circ L</math>
| <math>T\!</math>
|
| <math>W\!</math>
| <math>V\!</math>
|}
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 13. Another Brand of Composition
o---------o---------o---------o---------o
| # !1! | !1! | !1! |
o=========o=========o=========o=========o
| G # X | Y | Z |
o---------o---------o---------o---------o
| T # | Y | Z |
o---------o---------o---------o---------o
| G o T # X | | Z |
o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:60%"
|+ <math>\text{Table 13. Another Brand of Composition}\!</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
|-
| style="border-right:1px solid black" | <math>G\!</math>
| <math>X\!</math>
| <math>Y\!</math>
| <math>Z\!</math>
|-
| style="border-right:1px solid black" | <math>T\!</math>
|
| <math>Y\!</math>
| <math>Z\!</math>
|-
| style="border-right:1px solid black" | <math>G \circ T</math>
| <math>X\!</math>
|
| <math>Z\!</math>
|}
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 15. Conjunction Via Composition
o---------o---------o---------o---------o
| # !1! | !1! | !1! |
o=========o=========o=========o=========o
| L, # X | X | Y |
o---------o---------o---------o---------o
| S # | X | Y |
o---------o---------o---------o---------o
| L , S # X | | Y |
o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:60%"
|+ <math>\text{Table 15. Conjunction Via Composition}\!</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
|-
| style="border-right:1px solid black" | <math>L,\!</math>
| <math>X\!</math>
| <math>X\!</math>
| <math>Y\!</math>
|-
| style="border-right:1px solid black" | <math>S\!</math>
|
| <math>X\!</math>
| <math>Y\!</math>
|-
| style="border-right:1px solid black" | <math>L,\!S</math>
| <math>X\!</math>
|
| <math>Y\!</math>
|}
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 18. Relational Composition P o Q
o---------o---------o---------o---------o
| # !1! | !1! | !1! |
o=========o=========o=========o=========o
| P # X | Y | |
o---------o---------o---------o---------o
| Q # | Y | Z |
o---------o---------o---------o---------o
| P o Q # X | | Z |
o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:60%"
|+ <math>\text{Table 18. Relational Composition}~ P \circ Q</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
|-
| style="border-right:1px solid black" | <math>P\!</math>
| <math>X\!</math>
| <math>Y\!</math>
|
|-
| style="border-right:1px solid black" | <math>Q\!</math>
|
| <math>Y\!</math>
| <math>Z\!</math>
|-
| style="border-right:1px solid black" | <math>P \circ Q</math>
| <math>X\!</math>
|
| <math>Z\!</math>
|}
<br>
{| align="center" cellspacing="6" width="90%"
| align="center" |
<pre>
Table 20. Arrow: J(L(u, v)) = K(Ju, Jv)
o---------o---------o---------o---------o
| # J | J | J |
o=========o=========o=========o=========o
| K # X | X | X |
o---------o---------o---------o---------o
| L # Y | Y | Y |
o---------o---------o---------o---------o
</pre>
|}
<br>
{| align="center" cellpadding="10" 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; width:60%"
|+ <math>\text{Table 20. Arrow Equation:}~~ J(L(u, v)) = K(Ju, Jv)</math>
|-
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" |
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
|-
| style="border-right:1px solid black" | <math>K\!</math>
| <math>X\!</math>
| <math>X\!</math>
| <math>X\!</math>
|-
| style="border-right:1px solid black" | <math>L\!</math>
| <math>Y\!</math>
| <math>Y\!</math>
| <math>Y\!</math>
|}
<br>
==Grammar Stuff==
==Grammar Stuff==
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
| width="20%" | <math>\operatorname{Sentence}</math>
| width="20%" | <math>\operatorname{Sentence}</math>
| width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Parse}}</math>
| width="20%" | <math>\xrightarrow[\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}]{\operatorname{Parse}}</math>
| width="20%" | <math>\operatorname{Graph}</math>
| width="20%" | <math>\operatorname{Graph}</math>
| width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Denotation}}</math>
| width="20%" | <math>\xrightarrow[\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}]{\operatorname{Denotation}}</math>
| width="20%" | <math>\operatorname{Proposition}</math>
| width="20%" | <math>\operatorname{Proposition}</math>
|}
|}
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>s_j\!</math>
| width="20%" | <math>s_j\!</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>C_j\!</math>
| width="20%" | <math>C_j\!</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>q_j\!</math>
| width="20%" | <math>q_j\!</math>
|}
|}
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\operatorname{Conc}^0</math>
| width="20%" | <math>\operatorname{Conc}^0</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Node}^0</math>
| width="20%" | <math>\operatorname{Node}^0</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\underline{1}</math>
| width="20%" | <math>\underline{1}</math>
|-
|-
| width="20%" | <math>\operatorname{Conc}^k_j s_j</math>
| width="20%" | <math>\operatorname{Conc}^k_j s_j</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Node}^k_j C_j</math>
| width="20%" | <math>\operatorname{Node}^k_j C_j</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Conj}^k_j q_j</math>
| width="20%" | <math>\operatorname{Conj}^k_j q_j</math>
|}
|}
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
| width="20%" | <math>\operatorname{Surc}^0</math>
| width="20%" | <math>\operatorname{Surc}^0</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Lobe}^0</math>
| width="20%" | <math>\operatorname{Lobe}^0</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\underline{0}</math>
| width="20%" | <math>\underline{0}</math>
|-
|-
| width="20%" | <math>\operatorname{Surc}^k_j s_j</math>
| width="20%" | <math>\operatorname{Surc}^k_j s_j</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Lobe}^k_j C_j</math>
| width="20%" | <math>\operatorname{Lobe}^k_j C_j</math>
| width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math>
| width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
| width="20%" | <math>\operatorname{Surj}^k_j q_j</math>
| width="20%" | <math>\operatorname{Surj}^k_j q_j</math>
|}
|}
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
|+ '''Table 15. Boolean Functions on Zero Variables'''
|+ '''Table 15. Boolean Functions on Zero Variables'''
|- style="background:ghostwhite"
|- style="background:whitesmoke"
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| <math>F_0^{(0)}\!</math>
| <math>F_0^{(0)}\!</math>
| <math>\underline{0}</math>
| <math>\underline{0}</math>
| <math>\underline{(} ~ \underline{)}</math>
| <math>(~)</math>
|-
|-
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>F_1^{(0)}\!</math>
| <math>F_1^{(0)}\!</math>
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>\underline{((} ~ \underline{))}</math>
| <math>((~))</math>
|}
|}
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:90%"
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:90%"
|+ '''Table 16. Boolean Functions on One Variable'''
|+ '''Table 16. Boolean Functions on One Variable'''
|- style="background:ghostwhite"
|- style="background:whitesmoke"
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| colspan="2" | <math>F(x)\!</math>
| colspan="2" | <math>F(x)\!</math>
| width="24%" | <math>F\!</math>
| width="24%" | <math>F\!</math>
|- style="background:ghostwhite"
|- style="background:whitesmoke"
| width="14%" |
| width="14%" |
| width="14%" |
| width="14%" |
| <math>\underline{0}</math>
| <math>\underline{0}</math>
| <math>\underline{0}</math>
| <math>\underline{0}</math>
| <math>\underline{(} ~ \underline{)}</math>
| <math>(~)</math>
|-
|-
| <math>F_1^{(1)}\!</math>
| <math>F_1^{(1)}\!</math>
| <math>\underline{0}</math>
| <math>\underline{0}</math>
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>\underline{(} x \underline{)}</math>
| <math>(x)\!</math>
|-
|-
| <math>F_2^{(1)}\!</math>
| <math>F_2^{(1)}\!</math>
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>\underline{1}</math>
| <math>\underline{((} ~ \underline{))}</math>
| <math>((~))</math>
|}
|}
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:90%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:90%"
|+ '''Table 17. Boolean Functions on Two Variables'''
|+ '''Table 17. Boolean Functions on Two Variables'''
|- style="background:ghostwhite"
|- style="background:whitesmoke"
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| width="14%" | <math>F\!</math>
| colspan="4" | <math>F(x, y)\!</math>
| colspan="4" | <math>F(x, y)\!</math>
| width="24%" | <math>F\!</math>
| width="24%" | <math>F\!</math>
|- style="background:ghostwhite"
|- style="background:whitesmoke"
| width="14%" |
| width="14%" |
| width="14%" |
| width="14%" |
