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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 16:32, 2 May 2009
, 16:32, 2 May 2009→Commentary Note 12.1
| height="60" | <math>\mathfrak{L}^\mathfrak{W} ~=~ \operatorname{Mat}(\mathit{l})^{\operatorname{Mat}(\mathrm{w})} ~=~ \operatorname{Mat}(\mathit{l}^\mathrm{w})</math>
| height="60" | <math>\mathfrak{L}^\mathfrak{W} ~=~ \operatorname{Mat}(\mathit{l})^{\operatorname{Mat}(\mathrm{w})} ~=~ \operatorname{Mat}(\mathit{l}^\mathrm{w})</math>
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Because <math>\mathit{l}^\mathrm{w}\!</math> denotes the elements of a subset of <math>X\!</math> the matrix <math>\mathfrak{L}^\mathfrak{W}</math> is a 1-dimensional array of coefficients in <math>\mathbb{B}</math> that is indexed by the elements of <math>X.\!</math> The value of the matrix <math>\mathfrak{L}^\mathfrak{W}</math> at the index <math>a \in X</math> is written <math>(\mathfrak{L}^\mathfrak{W})_a</math> and computed as follows:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_{a} ~=~ \prod_{x \in X} \mathfrak{L}_{ax}^{\mathfrak{W}_{x}}</math>
| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_a ~=~ \prod_{x \in X} \mathfrak{L}_{ax}^{\mathfrak{W}_{x}}</math>
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