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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 15:52, 15 April 2009
, 15:52, 15 April 2009→Commentary Note 11.12
For a 2-adic relation <math>L \subseteq X \times Y,</math> we have:
For a 2-adic relation <math>L \subseteq X \times Y,</math> we have:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" style="text-align:center" width="90%"
|
|
<math>\begin{array}{lll}
<math>\begin{array}{lll}
|}
|}
As for the definition of relational composition, it is enough to consider the coefficient of the composite on an arbitrary ordered pair like ''i'':''j''.
As for the definition of relational composition, it is enough to consider the coefficient of the composite on an arbitrary ordered pair like <math>i:j.\!</math>
: (''P'' o ''Q'')<sub>''ij''</sub> = ∑<sub>''k''</sub> (''P''<sub>''ik''</sub> ''Q''<sub>''kj''</sub>).
{| align="center" cellspacing="6" style="text-align:center" width="90%"
| <math>(P \circ Q)_{ij} ~=~ \sum_k P_{ik} Q_{kj}</math>
|}
So let us begin.
So let us begin.