Line 6,331: |
Line 6,331: |
| \end{tabular}\end{quote} | | \end{tabular}\end{quote} |
| </pre> | | </pre> |
| + | |
| + | ==Group Operation Tables== |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="0" 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:80%" |
| + | |+ <math>\text{Table 32.1}~~\text{Scheme of a Group Operation Table}</math> |
| + | |- style="height:50px" |
| + | | style="border-bottom:1px solid black; border-right:1px solid black" | <math>*\!</math> |
| + | | style="border-bottom:1px solid black" | <math>x_0\!</math> |
| + | | style="border-bottom:1px solid black" | <math>\cdots\!</math> |
| + | | style="border-bottom:1px solid black" | <math>x_j\!</math> |
| + | | style="border-bottom:1px solid black" | <math>\cdots\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_0\!</math> |
| + | | <math>x_0 * x_0\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>x_0 * x_j\!</math> |
| + | | <math>\cdots\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_i\!</math> |
| + | | <math>x_i * x_0\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>x_i * x_j\!</math> |
| + | | <math>\cdots\!</math> |
| + | |- style="height:50px" |
| + | | width="12%" style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="0" 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:80%" |
| + | |+ <math>\text{Table 32.2}~~\text{Scheme of the Regular Ante-Representation}</math> |
| + | |- style="height:50px" |
| + | | style="border-bottom:1px solid black; border-right:1px solid black" | <math>\text{Element}\!</math> |
| + | | colspan="6" style="border-bottom:1px solid black" | <math>\text{Function as Set of Ordered Pairs of Elements}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_0\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>(x_0 ~,~ x_0 * x_0),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>(x_j ~,~ x_0 * x_j),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_i\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>(x_0 ~,~ x_i * x_0),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>(x_j ~,~ x_i * x_j),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | width="12%" style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="18%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="18%" | <math>\cdots\!</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="0" 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:80%" |
| + | |+ <math>\text{Table 32.3}~~\text{Scheme of the Regular Post-Representation}</math> |
| + | |- style="height:50px" |
| + | | style="border-bottom:1px solid black; border-right:1px solid black" | <math>\text{Element}\!</math> |
| + | | colspan="6" style="border-bottom:1px solid black" | <math>\text{Function as Set of Ordered Pairs of Elements}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_0\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>(x_0 ~,~ x_0 * x_0),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>(x_j ~,~ x_j * x_0),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>x_i\!</math> |
| + | | <math>\{\!</math> |
| + | | <math>(x_0 ~,~ x_0 * x_i),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>(x_j ~,~ x_j * x_i),\!</math> |
| + | | <math>\cdots\!</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | width="12%" style="border-right:1px solid black" | <math>\cdots\!</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="18%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="22%" | <math>\cdots\!</math> |
| + | | width="18%" | <math>\cdots\!</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |} |
| + | |
| + | <br> |
| | | |
| ==Higher Order Propositions== | | ==Higher Order Propositions== |