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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 19:30, 17 April 2012
, 19:30, 17 April 2012→6.6. Basic Notions of Group Theory: markup
A '''relation''' is defined on a SOD as a subset of its cartesian product. In symbols, <math>L\!</math> is a relation on <math>(X_i),\!</math> if and only if <math>L \subseteq \textstyle\prod_i X_i.</math>
A '''relation''' is defined on a SOD as a subset of its cartesian product. In symbols, <math>L\!</math> is a relation on <math>(X_i),\!</math> if and only if <math>L \subseteq \textstyle\prod_i X_i.</math>
A '''<math>k\!</math>-ary relation''' or a '''<math>k\!</math>-place relation''' is a relation on an ordered <math>k\!</math>-tuple of nonempty sets. Thus, <math>L\!</math> is a <math>k\!</math>-place relation relation on the SOD <math>(X_1, \ldots, X_k)\!</math> if and only if <math>L \subseteq X_1 \times \ldots \times X_k.\!</math> In various applications, the <math>k\!</math>-tuple elements <math>(x_1, \ldots, x_k)\!</math> of <math>L\!</math> are called its ''elementary relations'', ''individual transactions'', ''ingredients'', or ''effects''.
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Before continuing with the chain of definitions, a slight digression is needed at this point to loosen up the interpretation of relation symbols in what follows. Exercising a certain amount of flexibility with notation, and relying on a discerning interpretation of equivocal expressions, one can use the name "R" or any other indication of an n place relation R in a wide variety of different fashions, both logical and operational.
Before continuing with the chain of definitions, a slight digression is needed at this point to loosen up the interpretation of relation symbols in what follows. Exercising a certain amount of flexibility with notation, and relying on a discerning interpretation of equivocal expressions, one can use the name "R" or any other indication of an n place relation R in a wide variety of different fashions, both logical and operational.