Changes

====Example 6====

====Example 6====

The discussion up to this point has developed two ways of computing a logical involution that raises a 2-adic relative term to the power of a 1-adic absolute term, for example, <math>\mathit{l}^\mathrm{w}\!</math> for "lover of every woman".

We now have two ways of computing a logical involution that raises a 2-adic relative term to the power of a 1-adic absolute term, for example, <math>\mathit{l}^\mathrm{w}\!</math> for "lover of every woman".

The first method operates in the medium of set theory, expressing the denotation of the term <math>\mathit{l}^\mathrm{w}\!</math> as the intersection of a set of relational applications:

The first method operates in the medium of set theory, expressing the denotation of the term <math>\mathit{l}^\mathrm{w}\!</math> as the intersection of a set of relational applications:

To highlight the role of <math>W\!</math> more clearly, the Figure represents the absolute term <math>^{\backprime\backprime} \mathrm{w} ^{\prime\prime}</math> by means of the relative term <math>^{\backprime\backprime} \mathrm{w}, ^{\prime\prime}</math> that conveys the same information.

To highlight the role of <math>W\!</math> more clearly, the Figure represents the absolute term <math>^{\backprime\backprime} \mathrm{w} ^{\prime\prime}</math> by means of the relative term <math>^{\backprime\backprime} \mathrm{w}, ^{\prime\prime}</math> that conveys the same information.

Computing the denotation of <math>\mathit{l}^\mathrm{w}\!</math> by means of the set-theoretic formula, we can show our work as follows:

Computing the denotation of <math>\mathit{l}^\mathrm{w}\!</math> by way of the set-theoretic formula, we can show our work as follows:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" width="90%"

As a general observation, 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>

As a general observation, 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===