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Revision as of 16:44, 4 February 2009
, 16:44, 4 February 2009→Derived Equivalence Relations: mathematical markup
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Equivalent expressions for this concept are recorded in Definition 10.
Equivalent expressions for this concept are recorded in Definition 10.
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D10e. {<o, s> C OxS : <o, s, i> C R for some i C I}
D10e. {<o, s> C OxS : <o, s, i> C R for some i C I}
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The dyadic relation RSO that constitutes the converse of the denotative relation ROS can be defined directly in the following fashion:
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The dyadic relation <math>L_{SO}\!</math> that is the converse of the denotative relation <math>L_{OS}\!</math> can be defined directly in the following fashion:
Den(R)^ = RSO = {<s, o> C SxO : <o, s, i> C R for some i C I}.
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| <math>\overset{\smile}{\operatorname{Den}(L)} ~=~ L_{SO} ~=~ \{ (s, o) \in S \times O ~:~ (o, s, i) \in L ~\text{for some}~ i \in I \}.</math>
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A few of the many different expressions for this concept are recorded in Definition 11.
A few of the many different expressions for this concept are recorded in Definition 11.
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Definition 11
Definition 11
D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}
D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}
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The "denotation of x in R", written "Den(R, x)", is defined as follows:
The "denotation of x in R", written "Den(R, x)", is defined as follows:
Den(R, x) = {o C O : <o, x> C Den(R)}.
Den(R, x) = {o C O : <o, x> C Den(R)}.