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Revision as of 16:40, 15 May 2013
, 16:40, 15 May 2013→6.43. Reflective Extensions: markup
Line 10,739:
Line 10,739:
+O = O<1> U O<2> = { A, B } U {<A>, <B>, <i>, <u>}.
−S = S<1> U S<2> = {<A>, <B>, <i>, <u>} U {<<A>>, <<B>>, <<i>>, <<u>>}.
−
Raised angle brackets or ''supercilia'' <math>({}^{\langle} \ldots {}^{\rangle})\!</math> are here being used on a par with ordinary quotation marks <math>({}^{\backprime\backprime} \ldots {}^{\prime\prime})\!</math> to construct a new sign whose object is precisely the sign they enclose.
Raised angle brackets or ''supercilia'' <math>({}^{\langle} \ldots {}^{\rangle})\!</math> are here being used on a par with ordinary quotation marks <math>({}^{\backprime\backprime} \ldots {}^{\prime\prime})\!</math> to construct a new sign whose object is precisely the sign they enclose.
−Regarded as sign relations in their own right, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> both have the following relational domains.
+Regarded as sign relations in their own right, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> are formed on the following relational domains.
+{| align="center" cellspacing="6" width="90%"
+|
+<math>\begin{array}{ccccl}
+O & = & O^{(1)} \cup O^{(2)} & = &
+\{ \text{A}, \text{B} \}
+~ \cup ~
+\{
+{}^{\langle} \text{A} {}^{\rangle},
+{}^{\langle} \text{B} {}^{\rangle},
+{}^{\langle} \text{i} {}^{\rangle},
+{}^{\langle} \text{u} {}^{\rangle}
+\}
+\\[8pt]
+S & = & S^{(1)} \cup S^{(2)} & = &
+\{
+{}^{\langle} \text{A} {}^{\rangle},
+{}^{\langle} \text{B} {}^{\rangle},
+{}^{\langle} \text{i} {}^{\rangle},
+{}^{\langle} \text{u} {}^{\rangle}
+\}
+~ \cup ~
+\{
+{}^{\langle\langle} \text{A} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{B} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{i} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+\}
+\\[8pt]
+I & = & I^{(1)} \cup I^{(2)} & = &
+\{
+{}^{\langle} \text{A} {}^{\rangle},
+{}^{\langle} \text{B} {}^{\rangle},
+{}^{\langle} \text{i} {}^{\rangle},
+{}^{\langle} \text{u} {}^{\rangle}
+\}
+~ \cup ~
+\{
+{}^{\langle\langle} \text{A} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{B} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{i} {}^{\rangle\rangle},
+{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+\}
+\end{array}</math>
+|}
<pre>
<pre>
−Thus, S overlaps with O in the set of first order signs or second order objects S<1> = O<2>, exemplifying the extent to which signs have become objects in the new sign relations.
Thus, S overlaps with O in the set of first order signs or second order objects S<1> = O<2>, exemplifying the extent to which signs have become objects in the new sign relations.
