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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 18:44, 2 May 2009
, 18:44, 2 May 2009→Commentary Note 12.1
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The fact that <math>\mathit{l}^\mathrm{w}\!</math> denotes the elements of a subset of <math>X\!</math> means that 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:
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{| 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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The meaning of a formula like that is more easily grasped with the aid of a freely chosen example and a picture of the relations involved.
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<pre>
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o o o o o o o o o X
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| | W,
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o o o o o o o o o X
\ \ / / \ / \ \ / /
\ \ / \ / \ \ / L
\ / \ / \ / \ / \ /
o o o o o o o o o X
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</pre>
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