Line 5,525: |
Line 5,525: |
| {| 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:60%" | | {| 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:60%" |
| |- style="height:50px" | | |- style="height:50px" |
− | | width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot</math> | + | | width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math> |
| | width="22%" style="border-bottom:1px solid black" | | | | width="22%" style="border-bottom:1px solid black" | |
| <math>\operatorname{T}_{00}</math> | | <math>\operatorname{T}_{00}</math> |
Line 5,564: |
Line 5,564: |
| {| 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:60%" | | {| 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:60%" |
| |- style="height:50px" | | |- style="height:50px" |
− | | width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot</math> | + | | width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math> |
| | width="22%" style="border-bottom:1px solid black" | | | | width="22%" style="border-bottom:1px solid black" | |
| <math>\operatorname{e}</math> | | <math>\operatorname{e}</math> |
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> |
| + | |
| + | {| 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:60%" |
| + | |+ <math>\text{Table 33.1}~~\text{Multiplication Operation of the Group}~V_4</math> |
| + | |- style="height:50px" |
| + | | width="20%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{e}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{f}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{g}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{h}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{e}</math> |
| + | | <math>\operatorname{e}</math> |
| + | | <math>\operatorname{f}</math> |
| + | | <math>\operatorname{g}</math> |
| + | | <math>\operatorname{h}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{f}</math> |
| + | | <math>\operatorname{f}</math> |
| + | | <math>\operatorname{e}</math> |
| + | | <math>\operatorname{h}</math> |
| + | | <math>\operatorname{g}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{g}</math> |
| + | | <math>\operatorname{g}</math> |
| + | | <math>\operatorname{h}</math> |
| + | | <math>\operatorname{e}</math> |
| + | | <math>\operatorname{f}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{h}</math> |
| + | | <math>\operatorname{h}</math> |
| + | | <math>\operatorname{g}</math> |
| + | | <math>\operatorname{f}</math> |
| + | | <math>\operatorname{e}</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:60%" |
| + | |+ <math>\text{Table 33.2}~~\text{Regular Representation of the Group}~V_4</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" |
| + | | width="20%" style="border-right:1px solid black" | <math>\operatorname{e}</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="16%" | <math>(\operatorname{e}, \operatorname{e}),</math> |
| + | | width="20%" | <math>(\operatorname{f}, \operatorname{f}),</math> |
| + | | width="20%" | <math>(\operatorname{g}, \operatorname{g}),</math> |
| + | | width="16%" | <math>(\operatorname{h}, \operatorname{h})</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{f}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{e}, \operatorname{f}),</math> |
| + | | <math>(\operatorname{f}, \operatorname{e}),</math> |
| + | | <math>(\operatorname{g}, \operatorname{h}),</math> |
| + | | <math>(\operatorname{h}, \operatorname{g})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{g}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{e}, \operatorname{g}),</math> |
| + | | <math>(\operatorname{f}, \operatorname{h}),</math> |
| + | | <math>(\operatorname{g}, \operatorname{e}),</math> |
| + | | <math>(\operatorname{h}, \operatorname{f})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{h}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{e}, \operatorname{h}),</math> |
| + | | <math>(\operatorname{f}, \operatorname{g}),</math> |
| + | | <math>(\operatorname{g}, \operatorname{f}),</math> |
| + | | <math>(\operatorname{h}, \operatorname{e})</math> |
| + | | <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:60%" |
| + | |+ <math>\text{Table 33.3}~~\text{Regular Representation of the Group}~V_4</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 Symbols}\!</math> |
| + | |- style="height:50px" |
| + | | width="20%" style="border-right:1px solid black" | <math>\operatorname{e}</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="16%" | <math>({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),</math> |
| + | | width="20%" | <math>({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),</math> |
| + | | width="20%" | <math>({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),</math> |
| + | | width="16%" | <math>({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime})</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{f}</math> |
| + | | <math>\{\!</math> |
| + | | <math>({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{g}</math> |
| + | | <math>\{\!</math> |
| + | | <math>({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{h}</math> |
| + | | <math>\{\!</math> |
| + | | <math>({}^{\backprime\backprime}\text{e}{}^{\prime\prime}, {}^{\backprime\backprime}\text{h}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{f}{}^{\prime\prime}, {}^{\backprime\backprime}\text{g}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{g}{}^{\prime\prime}, {}^{\backprime\backprime}\text{f}{}^{\prime\prime}),</math> |
| + | | <math>({}^{\backprime\backprime}\text{h}{}^{\prime\prime}, {}^{\backprime\backprime}\text{e}{}^{\prime\prime})</math> |
| + | | <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:60%" |
| + | |+ <math>\text{Table 34.1}~~\text{Multiplicative Presentation of the Group}~Z_4(\cdot)</math> |
| + | |- style="height:50px" |
| + | | width="20%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot\!</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{1}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{a}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{b}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{c}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{a}</math> |
| + | | <math>\operatorname{b}</math> |
| + | | <math>\operatorname{c}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{a}</math> |
| + | | <math>\operatorname{a}</math> |
| + | | <math>\operatorname{b}</math> |
| + | | <math>\operatorname{c}</math> |
| + | | <math>\operatorname{1}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{b}</math> |
| + | | <math>\operatorname{b}</math> |
| + | | <math>\operatorname{c}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{a}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{c}</math> |
| + | | <math>\operatorname{c}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{a}</math> |
| + | | <math>\operatorname{b}</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:60%" |
| + | |+ <math>\text{Table 34.2}~~\text{Regular Representation of the Group}~Z_4(\cdot)</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" |
| + | | width="20%" style="border-right:1px solid black" | <math>\operatorname{1}</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="16%" | <math>(\operatorname{1}, \operatorname{1}),</math> |
| + | | width="20%" | <math>(\operatorname{a}, \operatorname{a}),</math> |
| + | | width="20%" | <math>(\operatorname{b}, \operatorname{b}),</math> |
| + | | width="16%" | <math>(\operatorname{c}, \operatorname{c})</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{a}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{1}, \operatorname{a}),</math> |
| + | | <math>(\operatorname{a}, \operatorname{b}),</math> |
| + | | <math>(\operatorname{b}, \operatorname{c}),</math> |
| + | | <math>(\operatorname{c}, \operatorname{1})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{b}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{1}, \operatorname{b}),</math> |
| + | | <math>(\operatorname{a}, \operatorname{c}),</math> |
| + | | <math>(\operatorname{b}, \operatorname{1}),</math> |
| + | | <math>(\operatorname{c}, \operatorname{a})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{c}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{1}, \operatorname{c}),</math> |
| + | | <math>(\operatorname{a}, \operatorname{1}),</math> |
| + | | <math>(\operatorname{b}, \operatorname{a}),</math> |
| + | | <math>(\operatorname{c}, \operatorname{b})</math> |
| + | | <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:60%" |
| + | |+ <math>\text{Table 35.1}~~\text{Additive Presentation of the Group}~Z_4(+)</math> |
| + | |- style="height:50px" |
| + | | width="20%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>+\!</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{0}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{1}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{2}</math> |
| + | | width="20%" style="border-bottom:1px solid black" | <math>\operatorname{3}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{0}</math> |
| + | | <math>\operatorname{0}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{2}</math> |
| + | | <math>\operatorname{3}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{2}</math> |
| + | | <math>\operatorname{3}</math> |
| + | | <math>\operatorname{0}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{2}</math> |
| + | | <math>\operatorname{2}</math> |
| + | | <math>\operatorname{3}</math> |
| + | | <math>\operatorname{0}</math> |
| + | | <math>\operatorname{1}</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{3}</math> |
| + | | <math>\operatorname{3}</math> |
| + | | <math>\operatorname{0}</math> |
| + | | <math>\operatorname{1}</math> |
| + | | <math>\operatorname{2}</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:60%" |
| + | |+ <math>\text{Table 35.2}~~\text{Regular Representation of the Group}~Z_4(+)</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" |
| + | | width="20%" style="border-right:1px solid black" | <math>\operatorname{0}</math> |
| + | | width="4%" | <math>\{\!</math> |
| + | | width="16%" | <math>(\operatorname{0}, \operatorname{0}),</math> |
| + | | width="20%" | <math>(\operatorname{1}, \operatorname{1}),</math> |
| + | | width="20%" | <math>(\operatorname{2}, \operatorname{2}),</math> |
| + | | width="16%" | <math>(\operatorname{3}, \operatorname{3})</math> |
| + | | width="4%" | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{1}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{0}, \operatorname{1}),</math> |
| + | | <math>(\operatorname{1}, \operatorname{2}),</math> |
| + | | <math>(\operatorname{2}, \operatorname{3}),</math> |
| + | | <math>(\operatorname{3}, \operatorname{0})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{2}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{0}, \operatorname{2}),</math> |
| + | | <math>(\operatorname{1}, \operatorname{3}),</math> |
| + | | <math>(\operatorname{2}, \operatorname{0}),</math> |
| + | | <math>(\operatorname{3}, \operatorname{1})</math> |
| + | | <math>\}\!</math> |
| + | |- style="height:50px" |
| + | | style="border-right:1px solid black" | <math>\operatorname{3}</math> |
| + | | <math>\{\!</math> |
| + | | <math>(\operatorname{0}, \operatorname{3}),</math> |
| + | | <math>(\operatorname{1}, \operatorname{0}),</math> |
| + | | <math>(\operatorname{2}, \operatorname{1}),</math> |
| + | | <math>(\operatorname{3}, \operatorname{2})</math> |
| + | | <math>\}\!</math> |
| + | |} |
| + | |
| + | <br> |
| | | |
| ==Higher Order Propositions== | | ==Higher Order Propositions== |