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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 03:32, 3 May 2009
, 03:32, 3 May 2009→Commentary Note 12.1
| If any of the values <math>\mathfrak{L}_{ux}^{\mathfrak{W}_x}</math> is <math>0\!</math> then the product <math>\textstyle\prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_x}</math> is <math>0,\!</math> otherwise it is <math>1.\!</math>
| If any of the values <math>\mathfrak{L}_{ux}^{\mathfrak{W}_x}</math> is <math>0\!</math> then the product <math>\textstyle\prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_x}</math> is <math>0,\!</math> otherwise it is <math>1.\!</math>
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As a general observation, then, we know that the value of <math>(\mathfrak{L}^\mathfrak{W})_u</math> goes to <math>0\!</math> just as soon as we find an <math>x \in X</math> such that <math>\mathfrak{L}_{ux} = 0</math> and <math>\mathfrak{W}_x = 1,</math> in other words, such that <math>(u, x) \notin L</math> but <math>u \in W.</math> If there is no such <math>x\!</math> then <math>(\mathfrak{L}^\mathfrak{W})_u = 1.</math>
===Commentary Note 12.2===
===Commentary Note 12.2===