Line 1: |
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| + | <div class="nonumtoc">__TOC__</div> |
| + | |
| + | ==Tables== |
| + | |
| + | ===Boolean Functions and Propositional Calculus=== |
| + | |
| + | * Examples of LaTeX tabular markup from [http://inquiryintoinquiry.com/tables/ Inquiry Into Inquiry • Tables] |
| + | |
| + | <pre> |
| + | $latex |
| + | \begin{tabular}{|*{7}{c|}} |
| + | \multicolumn{7}{c}{Table A1. Propositional Forms on Two Variables} \\ |
| + | \hline |
| + | \(L_1\)&\(L_2\)&&\(L_3\)&\(L_4\)&\(L_5\)&\(L_6\) \\ |
| + | \hline |
| + | &&\(x=\)&1 1 0 0&&& \\ |
| + | &&\(y=\)&1 0 1 0&&& \\ |
| + | \hline |
| + | \(f_{0}\)& |
| + | \(f_{0000}\)&& |
| + | 0 0 0 0& |
| + | \((~)\)& |
| + | false& |
| + | \(0\) |
| + | \\ |
| + | \(f_{1}\)& |
| + | \(f_{0001}\)&& |
| + | 0 0 0 1& |
| + | \((x)(y)\)& |
| + | neither \(x\) nor \(y\)& |
| + | \(\lnot x \land \lnot y\) |
| + | \\ |
| + | \(f_{2}\)& |
| + | \(f_{0010}\)&& |
| + | 0 0 1 0& |
| + | \((x)~y~\)& |
| + | \(y\) without \(x\)& |
| + | \(\lnot x \land y\) |
| + | \\ |
| + | \(f_{3}\)& |
| + | \(f_{0011}\)&& |
| + | 0 0 1 1& |
| + | \((x)\)& |
| + | not \(x\)& |
| + | \(\lnot x\) |
| + | \\ |
| + | \(f_{4}\)& |
| + | \(f_{0100}\)&& |
| + | 0 1 0 0& |
| + | \(~x~(y)\)& |
| + | \(x\) without \(y\)& |
| + | \(x \land \lnot y\) |
| + | \\ |
| + | \(f_{5}\)& |
| + | \(f_{0101}\)&& |
| + | 0 1 0 1& |
| + | \((y)\)& |
| + | not \(y\)& |
| + | \(\lnot y\) |
| + | \\ |
| + | \(f_{6}\)& |
| + | \(f_{0110}\)&& |
| + | 0 1 1 0& |
| + | \((x,~y)\)& |
| + | \(x\) not equal to \(y\)& |
| + | \(x \ne y\) |
| + | \\ |
| + | \(f_{7}\)& |
| + | \(f_{0111}\)&& |
| + | 0 1 1 1& |
| + | \((x~~y)\)& |
| + | not both \(x\) and \(y\)& |
| + | \(\lnot x \lor \lnot y\) |
| + | \\ |
| + | \hline |
| + | \(f_{8}\)& |
| + | \(f_{1000}\)&& |
| + | 1 0 0 0& |
| + | \(~x~~y~\)& |
| + | \(x\) and \(y\)& |
| + | \(x \land y\) |
| + | \\ |
| + | \(f_{9}\)& |
| + | \(f_{1001}\)&& |
| + | 1 0 0 1& |
| + | \(((x,~y))\)& |
| + | \(x\) equal to \(y\)& |
| + | \(x = y\) |
| + | \\ |
| + | \(f_{10}\)& |
| + | \(f_{1010}\)&& |
| + | 1 0 1 0& |
| + | \(y\)& |
| + | \(y\)& |
| + | \(y\) |
| + | \\ |
| + | \(f_{11}\)& |
| + | \(f_{1011}\)&& |
| + | 1 0 1 1& |
| + | \((~x~(y))\)& |
| + | not \(x\) without \(y\)& |
| + | \(x \Rightarrow y\) |
| + | \\ |
| + | \(f_{12}\)& |
| + | \(f_{1100}\)&& |
| + | 1 1 0 0& |
| + | \(x\)& |
| + | \(x\)& |
| + | \(x\) |
| + | \\ |
| + | \(f_{13}\)& |
| + | \(f_{1101}\)&& |
| + | 1 1 0 1& |
| + | \(((x)~y~)\)& |
| + | not \(y\) without \(x\)& |
| + | \(x \Leftarrow y\) |
| + | \\ |
| + | \(f_{14}\)& |
| + | \(f_{1110}\)&& |
| + | 1 1 1 0& |
| + | \(((x)(y))\)& |
| + | \(x\) or \(y\)& |
| + | \(x \lor y\) |
| + | \\ |
| + | \(f_{15}\)& |
| + | \(f_{1111}\)&& |
| + | 1 1 1 1& |
| + | \(((~))\)& |
| + | true& |
| + | \(1\) |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | </pre> |
| + | |
| + | <pre> |
| + | $latex |
| + | \begin{tabular}{|*{7}{c|}} |
| + | \multicolumn{7}{c}{Table A2. Propositional Forms on Two Variables} \\ |
| + | \hline |
| + | \(L_1\)&\(L_2\)&&\(L_3\)&\(L_4\)&\(L_5\)&\(L_6\) \\ |
| + | \hline |
| + | &&\(x =\)&1 1 0 0&&& \\ |
| + | &&\(y =\)&1 0 1 0&&& \\ |
| + | \hline |
| + | \(f_{0}\)& |
| + | \(f_{0000}\)&& |
| + | 0 0 0 0& |
| + | \((~)\)& |
| + | false& |
| + | \(0\) |
| + | \\ |
| + | \hline |
| + | \(f_{1}\)& |
| + | \(f_{0001}\)&& |
| + | 0 0 0 1& |
| + | \((x)(y)\)& |
| + | neither \(x\) nor \(y\)& |
| + | \(\lnot x \land \lnot y\) |
| + | \\ |
| + | \(f_{2}\)& |
| + | \(f_{0010}\)&& |
| + | 0 0 1 0& |
| + | \((x)~y~\)& |
| + | \(y\) without \(x\)& |
| + | \(\lnot x \land y\) |
| + | \\ |
| + | \(f_{4}\)& |
| + | \(f_{0100}\)&& |
| + | 0 1 0 0& |
| + | \(~x~(y)\)& |
| + | \(x\) without \(y\)& |
| + | \(x \land \lnot y\) |
| + | \\ |
| + | \(f_{8}\)& |
| + | \(f_{1000}\)&& |
| + | 1 0 0 0& |
| + | \(~x~~y~\)& |
| + | \(x\) and \(y\)& |
| + | \(x \land y\) |
| + | \\ |
| + | \hline |
| + | \(f_{3}\)& |
| + | \(f_{0011}\)&& |
| + | 0 0 1 1& |
| + | \((x)\)& |
| + | not \(x\)& |
| + | \(\lnot x\) |
| + | \\ |
| + | \(f_{12}\)& |
| + | \(f_{1100}\)&& |
| + | 1 1 0 0& |
| + | \(x\)& |
| + | \(x\)& |
| + | \(x\) |
| + | \\ |
| + | \hline |
| + | \(f_{6}\)& |
| + | \(f_{0110}\)&& |
| + | 0 1 1 0& |
| + | \((x,~y)\)& |
| + | \(x\) not equal to \(y\)& |
| + | \(x \ne y\) |
| + | \\ |
| + | \(f_{9}\)& |
| + | \(f_{1001}\)&& |
| + | 1 0 0 1& |
| + | \(((x,~y))\)& |
| + | \(x\) equal to \(y\)& |
| + | \(x = y\) |
| + | \\ |
| + | \hline |
| + | \(f_{5}\)& |
| + | \(f_{0101}\)&& |
| + | 0 1 0 1& |
| + | \((y)\)& |
| + | not \(y\)& |
| + | \(\lnot y\) |
| + | \\ |
| + | \(f_{10}\)& |
| + | \(f_{1010}\)&& |
| + | 1 0 1 0& |
| + | \(y\)& |
| + | \(y\)& |
| + | \(y\) |
| + | \\ |
| + | \hline |
| + | \(f_{7}\)& |
| + | \(f_{0111}\)&& |
| + | 0 1 1 1& |
| + | \((~x~~y~)\)& |
| + | not both \(x\) and \(y\)& |
| + | \(\lnot x \lor \lnot y\) |
| + | \\ |
| + | \(f_{11}\)& |
| + | \(f_{1011}\)&& |
| + | 1 0 1 1& |
| + | \((~x~(y))\)& |
| + | not \(x\) without \(y\)& |
| + | \(x \Rightarrow y\) |
| + | \\ |
| + | \(f_{13}\)& |
| + | \(f_{1101}\)&& |
| + | 1 1 0 1& |
| + | \(((x)~y~)\)& |
| + | not \(y\) without \(x\)& |
| + | \(x \Leftarrow y\) |
| + | \\ |
| + | \(f_{14}\)& |
| + | \(f_{1110}\)&& |
| + | 1 1 1 0& |
| + | \(((x)(y))\)& |
| + | \(x\) or \(y\)& |
| + | \(x \lor y\) |
| + | \\ |
| + | \hline |
| + | \(f_{15}\)& |
| + | \(f_{1111}\)&& |
| + | 1 1 1 1& |
| + | \(((~))\)& |
| + | true& |
| + | \(1\) |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | </pre> |
| + | |
| + | <pre> |
| + | $latex |
| + | \begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{Table A3. \(\mathrm{E}f\) Expanded Over Differential Features \(\{\mathrm{d}x, \mathrm{d}y\}\)} \\ |
| + | \hline |
| + | & |
| + | \(~~~~~~~~ f ~~~~~~~~\)& |
| + | \(~~~~\mathrm{T}_{11}f~~~~\)& |
| + | \(~~~~\mathrm{T}_{10}f~~~~\)& |
| + | \(~~~~\mathrm{T}_{01}f~~~~\)& |
| + | \(~~~~\mathrm{T}_{00}f~~~~\) |
| + | \\ |
| + | && |
| + | \(\mathrm{E}f|_{~\mathrm{d}x ~\mathrm{d}y~}~\)& |
| + | \(\mathrm{E}f|_{~\mathrm{d}x~(\mathrm{d}y)}~\)& |
| + | \(\mathrm{E}f|_{(\mathrm{d}x)~\mathrm{d}y~}~\)& |
| + | \(\mathrm{E}f|_{(\mathrm{d}x)(\mathrm{d}y)}~\) |
| + | \\ |
| + | \hline\hline |
| + | \(f_{0}\)& |
| + | \(0\)& |
| + | \(0\)& |
| + | \(0\)& |
| + | \(0\)& |
| + | \(0\) |
| + | \\ |
| + | \hline |
| + | \(f_{1}\)& |
| + | \((x)(y)\)& |
| + | \(~x~~y~\)& |
| + | \(~x~(y)\)& |
| + | \((x)~y~\)& |
| + | \((x)(y)\) |
| + | \\ |
| + | \(f_{2}\)& |
| + | \((x)~y~\)& |
| + | \(~x~(y)\)& |
| + | \(~x~~y~\)& |
| + | \((x)(y)\)& |
| + | \((x)~y~\) |
| + | \\ |
| + | \(f_{4}\)& |
| + | \(~x~(y)\)& |
| + | \((x)~y~\)& |
| + | \((x)(y)\)& |
| + | \(~x~~y~\)& |
| + | \(~x~(y)\) |
| + | \\ |
| + | \(f_{8}\)& |
| + | \(~x~~y~\)& |
| + | \((x)(y)\)& |
| + | \((x)~y~\)& |
| + | \(~x~(y)\)& |
| + | \(~x~~y~\) |
| + | \\ |
| + | \hline |
| + | \(f_{3}\)& |
| + | \((x)\)& |
| + | \( x \)& |
| + | \( x \)& |
| + | \((x)\)& |
| + | \((x)\) |
| + | \\ |
| + | \(f_{12}\)& |
| + | \( x \)& |
| + | \((x)\)& |
| + | \((x)\)& |
| + | \( x \)& |
| + | \( x \) |
| + | \\ |
| + | \hline |
| + | \(f_{6}\)& |
| + | \( (x,y) \)& |
| + | \( (x,y) \)& |
| + | \(((x,y))\)& |
| + | \(((x,y))\)& |
| + | \( (x,y) \) |
| + | \\ |
| + | \(f_{9}\)& |
| + | \(((x,y))\)& |
| + | \(((x,y))\)& |
| + | \( (x,y) \)& |
| + | \( (x,y) \)& |
| + | \(((x,y))\) |
| + | \\ |
| + | \hline |
| + | \(f_{5}\)& |
| + | \((y)\)& |
| + | \( y \)& |
| + | \((y)\)& |
| + | \( y \)& |
| + | \((y)\) |
| + | \\ |
| + | \(f_{10}\)& |
| + | \( y \)& |
| + | \((y)\)& |
| + | \( y \)& |
| + | \((y)\)& |
| + | \( y \) |
| + | \\ |
| + | \hline |
| + | \(f_{7}\)& |
| + | \((~x~~y~)\)& |
| + | \(((x)(y))\)& |
| + | \(((x)~y~)\)& |
| + | \((~x~(y))\)& |
| + | \((~x~~y~)\) |
| + | \\ |
| + | \(f_{11}\)& |
| + | \((~x~(y))\)& |
| + | \(((x)~y~)\)& |
| + | \(((x)(y))\)& |
| + | \((~x~~y~)\)& |
| + | \((~x~(y))\) |
| + | \\ |
| + | \(f_{13}\)& |
| + | \(((x)~y~)\)& |
| + | \((~x~(y))\)& |
| + | \((~x~~y~)\)& |
| + | \(((x)(y))\)& |
| + | \(((x)~y~)\) |
| + | \\ |
| + | \(f_{14}\)& |
| + | \(((x)(y))\)& |
| + | \((~x~~y~)\)& |
| + | \((~x~(y))\)& |
| + | \(((x)~y~)\)& |
| + | \(((x)(y))\) |
| + | \\ |
| + | \hline |
| + | \(f_{15}\)& |
| + | \(1\)& |
| + | \(1\)& |
| + | \(1\)& |
| + | \(1\)& |
| + | \(1\) |
| + | \\ |
| + | \hline\hline |
| + | \multicolumn{2}{|c||}{Fixed Point Total}& |
| + | 4& |
| + | 4& |
| + | 4& |
| + | 16 |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | </pre> |
| + | |
| + | <pre> |
| + | $latex |
| + | \begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{Table A4. \(\mathrm{D}f\) Expanded Over Differential Features \(\{\mathrm{d}x, \mathrm{d}y\}\)} \\ |
| + | \hline |
| + | & |
| + | \(~~~~~~~~ f ~~~~~~~~\)& |
| + | \(\mathrm{D}f|_{~\mathrm{d}x\;\mathrm{d}y~}~\)& |
| + | \(\mathrm{D}f|_{~\mathrm{d}x~(\mathrm{d}y)}~\)& |
| + | \(\mathrm{D}f|_{(\mathrm{d}x)~\mathrm{d}y~}~\)& |
| + | \(\mathrm{D}f|_{(\mathrm{d}x)(\mathrm{d}y)}~\) |
| + | \\ |
| + | \hline\hline |
| + | \( f_{0} \)& |
| + | \( 0 \)& |
| + | \( 0 \)& |
| + | \( 0 \)& |
| + | \( 0 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \( f_{1} \)& |
| + | \( (x)(y) \)& |
| + | \( ((x,y)) \)& |
| + | \( (y) \)& |
| + | \( (x) \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{2} \)& |
| + | \( (x)~y~ \)& |
| + | \( (x,y) \)& |
| + | \( y \)& |
| + | \( (x) \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{4} \)& |
| + | \( ~x~(y) \)& |
| + | \( (x,y) \)& |
| + | \( (y) \)& |
| + | \( x \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{8} \)& |
| + | \( ~x~~y~ \)& |
| + | \( ((x,y)) \)& |
| + | \( y \)& |
| + | \( x \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \( f_{3} \)& |
| + | \( (x) \)& |
| + | \( 1 \)& |
| + | \( 1 \)& |
| + | \( 0 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{12} \)& |
| + | \( x \)& |
| + | \( 1 \)& |
| + | \( 1 \)& |
| + | \( 0 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \( f_{6} \)& |
| + | \( (x,y) \)& |
| + | \( 0 \)& |
| + | \( 1 \)& |
| + | \( 1 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{9} \)& |
| + | \( ((x,y)) \)& |
| + | \( 0 \)& |
| + | \( 1 \)& |
| + | \( 1 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \( f_{5} \)& |
| + | \( (y) \)& |
| + | \( 1 \)& |
| + | \( 0 \)& |
| + | \( 1 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{10} \)& |
| + | \( y \)& |
| + | \( 1 \)& |
| + | \( 0 \)& |
| + | \( 1 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \( f_{7} \)& |
| + | \( (~x~~y~) \)& |
| + | \( ((x,y)) \)& |
| + | \( y \)& |
| + | \( x \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{11}\) & |
| + | \( (~x~(y)) \)& |
| + | \( (x,y) \)& |
| + | \( (y) \)& |
| + | \( x \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{13}\) & |
| + | \( ((x)~y~) \)& |
| + | \( (x,y) \)& |
| + | \( y \)& |
| + | \( (x) \)& |
| + | \( 0 \) |
| + | \\ |
| + | \( f_{14} \)& |
| + | \( ((x)(y)) \)& |
| + | \( ((x,y)) \)& |
| + | \( (y) \)& |
| + | \( (x) \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \(f_{15}\)& |
| + | \( 1 \)& |
| + | \( 0 \)& |
| + | \( 0 \)& |
| + | \( 0 \)& |
| + | \( 0 \) |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | </pre> |
| + | |
| + | <pre> |
| + | $latex |
| + | \begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{Table A5. \(\mathrm{E}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\ |
| + | \hline |
| + | & |
| + | \(~~~~~~~~ f ~~~~~~~~\)& |
| + | \(~~\mathrm{E}f|_{ x\;y }~~~\)& |
| + | \(~~\mathrm{E}f|_{ x~(y)}\,~~\)& |
| + | \(~~\mathrm{E}f|_{(x)~y }\,~~\)& |
| + | \(~~\mathrm{E}f|_{(x)(y)}\;~\) |
| + | \\ |
| + | \hline\hline |
| + | \(f_{0}\)& |
| + | 0& |
| + | 0& |
| + | 0& |
| + | 0& |
| + | 0 |
| + | \\ |
| + | \hline |
| + | \(f_{1}\)& |
| + | \((x)(y)\)& |
| + | ~d\(x\)~~d\(y~\)& |
| + | ~d\(x\)~(d\(y\))& |
| + | (d\(x\))~d\(y~\)& |
| + | (d\(x\))(d\(y\)) |
| + | \\ |
| + | \(f_{2}\)& |
| + | \((x)~y~\)& |
| + | ~d\(x\)~(d\(y\))& |
| + | ~d\(x\)~~d\(y~\)& |
| + | (d\(x\))(d\(y\))& |
| + | (d\(x\))~d\(y~\) |
| + | \\ |
| + | \(f_{4}\)& |
| + | \(~x~(y)\)& |
| + | (d\(x\))~d\(y~\)& |
| + | (d\(x\))(d\(y\))& |
| + | ~d\(x\)~~d\(y~\)& |
| + | ~d\(x\)~(d\(y\)) |
| + | \\ |
| + | \(f_{8}\)& |
| + | \(~x~~y~\)& |
| + | (d\(x\))(d\(y\))& |
| + | (d\(x\))~d\(y~\)& |
| + | ~d\(x\)~(d\(y\))& |
| + | ~d\(x\)~~d\(y~\) |
| + | \\ |
| + | \hline |
| + | \(f_{3}\)& |
| + | \((x)\)& |
| + | d\(x\) & |
| + | d\(x\) & |
| + | (d\(x\))& |
| + | (d\(x\)) |
| + | \\ |
| + | \(f_{12}\)& |
| + | \( x \)& |
| + | (d\(x\))& |
| + | (d\(x\))& |
| + | d\(x\) & |
| + | d\(x\) |
| + | \\ |
| + | \hline |
| + | \(f_{6}\)& |
| + | \( (x,y) \)& |
| + | (d\(x\), d\(y\)) & |
| + | ((d\(x\), d\(y\)))& |
| + | ((d\(x\), d\(y\)))& |
| + | (d\(x\), d\(y\)) |
| + | \\ |
| + | \(f_{9}\)& |
| + | \(((x,y))\)& |
| + | ((d\(x\), d\(y\)))& |
| + | (d\(x\), d\(y\)) & |
| + | (d\(x\), d\(y\)) & |
| + | ((d\(x\), d\(y\))) |
| + | \\ |
| + | \hline |
| + | \(f_{5}\)& |
| + | \((y)\)& |
| + | d\(y\) & |
| + | (d\(y\))& |
| + | d\(y\) & |
| + | (d\(y\)) |
| + | \\ |
| + | \(f_{10}\)& |
| + | \( y \)& |
| + | (d\(y\))& |
| + | d\(y\) & |
| + | (d\(y\))& |
| + | d\(y\) |
| + | \\ |
| + | \hline |
| + | \(f_{7}\)& |
| + | \((~x~~y~)\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ((d\(x\))~d\(y\)~)& |
| + | (~d\(x\)~(d\(y\)))& |
| + | (~d\(x\)~~d\(y\)~) |
| + | \\ |
| + | \(f_{11}\)& |
| + | \((~x~(y))\)& |
| + | ((d\(x\))~d\(y\)~)& |
| + | ((d\(x\))(d\(y\)))& |
| + | (~d\(x\)~~d\(y\)~)& |
| + | (~d\(x\)~(d\(y\))) |
| + | \\ |
| + | \(f_{13}\)& |
| + | \(((x)~y~)\)& |
| + | (~d\(x\)~(d\(y\)))& |
| + | (~d\(x\)~~d\(y\)~)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ((d\(x\))~d\(y\)~) |
| + | \\ |
| + | \(f_{14}\)& |
| + | \(((x)(y))\)& |
| + | (~d\(x\)~~d\(y\)~)& |
| + | (~d\(x\)~(d\(y\)))& |
| + | ((d\(x\))~d\(y\)~)& |
| + | ((d\(x\))(d\(y\))) |
| + | \\ |
| + | \hline |
| + | \(f_{15}\)& |
| + | 1& |
| + | 1& |
| + | 1& |
| + | 1& |
| + | 1 |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | |
| + | |
| + | $latex |
| + | \begin{tabular}{|c|c||c|c|c|c|} |
| + | \multicolumn{6}{c}{Table A6. \(\mathrm{D}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\ |
| + | \hline |
| + | & |
| + | \(~~~~~~~~ f ~~~~~~~~\)& |
| + | \(~~\mathrm{D}f|_{ x\;y }~~~\)& |
| + | \(~~\mathrm{D}f|_{ x~(y)}\,~~\)& |
| + | \(~~\mathrm{D}f|_{(x)~y }\,~~\)& |
| + | \(~~\mathrm{D}f|_{(x)(y)}\,~\) |
| + | \\ |
| + | \hline\hline |
| + | \(f_{0}\)& |
| + | 0& |
| + | 0& |
| + | 0& |
| + | 0& |
| + | 0 |
| + | \\ |
| + | \hline |
| + | \(f_{1}\)& |
| + | \((x)(y)\)& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | ((d\(x\))(d\(y\))) |
| + | \\ |
| + | \(f_{2}\)& |
| + | \((x)~y~\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~(d\(x\))~d\(y~~\) |
| + | \\ |
| + | \(f_{4}\)& |
| + | \(~x~(y)\)& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | ~~d\(x\)~(d\(y\))~ |
| + | \\ |
| + | \(f_{8}\)& |
| + | \(~x~~y~\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~~d\(x\)~~d\(y~~\) |
| + | \\ |
| + | \hline |
| + | \(f_{3}\)& |
| + | \((x)\)& |
| + | d\(x\)& |
| + | d\(x\)& |
| + | d\(x\)& |
| + | d\(x\) |
| + | \\ |
| + | \(f_{12}\)& |
| + | \( x \)& |
| + | d\(x\)& |
| + | d\(x\)& |
| + | d\(x\)& |
| + | d\(x\) |
| + | \\ |
| + | \hline |
| + | \(f_{6}\)& |
| + | \( (x,y) \)& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\)) |
| + | \\ |
| + | \(f_{9}\)& |
| + | \(((x,y))\)& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\))& |
| + | (d\(x\), d\(y\)) |
| + | \\ |
| + | \hline |
| + | \(f_{5}\)& |
| + | \((y)\)& |
| + | d\(y\)& |
| + | d\(y\)& |
| + | d\(y\)& |
| + | d\(y\) |
| + | \\ |
| + | \(f_{10}\)& |
| + | \( y \)& |
| + | d\(y\)& |
| + | d\(y\)& |
| + | d\(y\)& |
| + | d\(y\) |
| + | \\ |
| + | \hline |
| + | \(f_{7}\)& |
| + | \((~x~~y~)\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~~d\(x\)~~d\(y~~\) |
| + | \\ |
| + | \(f_{11}\)& |
| + | \((~x~(y))\)& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | ~~d\(x\)~(d\(y\))~ |
| + | \\ |
| + | \(f_{13}\)& |
| + | \(((x)~y~)\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | ((d\(x\))(d\(y\)))& |
| + | ~(d\(x\))~d\(y~~\) |
| + | \\ |
| + | \(f_{14}\)& |
| + | \(((x)(y))\)& |
| + | ~~d\(x\)~~d\(y~~\)& |
| + | \;d\(x\)~(d\(y\))~& |
| + | ~(d\(x\))~d\(y~~\)& |
| + | ((d\(x\))(d\(y\))) |
| + | \\ |
| + | \hline |
| + | \(f_{15}\)& |
| + | 1& |
| + | 0& |
| + | 0& |
| + | 0& |
| + | 0 |
| + | \\ |
| + | \hline |
| + | \end{tabular}&fg=000000$ |
| + | </pre> |
| + | |
| ==Work 2== | | ==Work 2== |
| | | |
− | * HTML and LaTeX markup examples from [http://inquiryintoinquiry.com/work/work-2/ Inquiry Into Inquiry • Work 2]. | + | * Examples of HTML and LaTeX markup from [http://inquiryintoinquiry.com/work/work-2/ Inquiry Into Inquiry • Work 2] |
| | | |
| ===Array Test=== | | ===Array Test=== |