MyWikiBiz, Author Your Legacy — Monday December 23, 2024
Jump to navigationJump to search
243 bytes added
, 00:36, 10 June 2009
Line 3,059: |
Line 3,059: |
| | | |
| {| align="center" cellpadding="6" width="90%" | | {| align="center" cellpadding="6" width="90%" |
− | | | + | | align="center" | |
| <math>\begin{bmatrix} | | <math>\begin{bmatrix} |
− | A:A & A:B & A:C | + | A\!:\!A & A\!:\!B & A\!:\!C |
| \\ | | \\ |
− | B:A & B:B & B:C | + | B\!:\!A & B\!:\!B & B\!:\!C |
| \\ | | \\ |
− | C:A & C:B & C:C | + | C\!:\!A & C\!:\!B & C\!:\!C |
| \end{bmatrix}</math> | | \end{bmatrix}</math> |
| |} | | |} |
Line 3,072: |
Line 3,072: |
| | | |
| {| align="center" cellpadding="6" width="90%" | | {| align="center" cellpadding="6" width="90%" |
− | | | + | | align="center" | |
| <math>\begin{bmatrix} | | <math>\begin{bmatrix} |
| e_{11} & e_{12} & e_{13} | | e_{11} & e_{12} & e_{13} |
Line 3,082: |
Line 3,082: |
| |} | | |} |
| | | |
− | So, for example, let us suppose that we have the small universe <math>\{ A, B, C \},\!</math> and the 2-adic relation <math>m = {}^{\backprime\backprime}\, \text{mover of}\, \underline{~~~~}\, {}^{\prime\prime}</math> that is represented by this matrix: | + | So, for example, let us suppose that we have the small universe <math>\{ A, B, C \},\!</math> and the 2-adic relation <math>m = {}^{\backprime\backprime}\, \text{mover of}\, \underline{~~~~}\, {}^{\prime\prime}</math> that is represented by the following matrix: |
| | | |
| {| align="center" cellpadding="6" width="90%" | | {| align="center" cellpadding="6" width="90%" |
− | | | + | | align="center" | |
− | <math> | + | <math>\begin{bmatrix} |
− | m ~=~
| + | m_{AA} (A\!:\!A) & m_{AB} (A\!:\!B) & m_{AC} (A\!:\!C) |
− | \begin{bmatrix} | |
− | m_{AA} (A:A) & m_{AB} (A:B) & m_{AC} (A:C) | |
| \\ | | \\ |
− | m_{BA} (B:A) & m_{BB} (B:B) & m_{BC} (B:C) | + | m_{BA} (B\!:\!A) & m_{BB} (B\!:\!B) & m_{BC} (B\!:\!C) |
| \\ | | \\ |
− | m_{CA} (C:A) & m_{CB} (C:B) & m_{CC} (C:C) | + | m_{CA} (C\!:\!A) & m_{CB} (C\!:\!B) & m_{CC} (C\!:\!C) |
− | \end{bmatrix} | + | \end{bmatrix}</math> |
− | </math> | |
| |} | | |} |
| | | |
Line 3,101: |
Line 3,098: |
| | | |
| {| align="center" cellpadding="6" width="90%" | | {| align="center" cellpadding="6" width="90%" |
− | | | + | | align="center" | |
| <math>\begin{array}{l} | | <math>\begin{array}{l} |
| A ~\text{is a mover of}~ A ~\text{and}~ B, | | A ~\text{is a mover of}~ A ~\text{and}~ B, |
Line 3,111: |
Line 3,108: |
| |} | | |} |
| | | |
− | In sum: | + | In sum, <math>m\!</math> is represented by the following matrix: |
| | | |
| {| align="center" cellpadding="6" width="90%" | | {| align="center" cellpadding="6" width="90%" |
− | | | + | | align="center" | |
− | <math> | + | <math>\begin{bmatrix} |
− | m ~=~
| + | 1 \cdot (A\!:\!A) & 1 \cdot (A\!:\!B) & 0 \cdot (A\!:\!C) |
− | \begin{bmatrix} | |
− | 1 \cdot (A:A) & 1 \cdot (A:B) & 0 \cdot (A:C) | |
| \\ | | \\ |
− | 0 \cdot (B:A) & 1 \cdot (B:B) & 1 \cdot (B:C) | + | 0 \cdot (B\!:\!A) & 1 \cdot (B\!:\!B) & 1 \cdot (B\!:\!C) |
| \\ | | \\ |
− | 1 \cdot (C:A) & 0 \cdot (C:B) & 1 \cdot (C:C) | + | 1 \cdot (C\!:\!A) & 0 \cdot (C\!:\!B) & 1 \cdot (C\!:\!C) |
− | \end{bmatrix} | + | \end{bmatrix}</math> |
− | </math> | |
| |} | | |} |
| | | |