Changes

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Often one's level of interest in a genre is ''purely generic''.  When the relevant genre is regarded as an indexed family of dyadic relations, ''G'' = {''G''_''j''}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.

Often one's level of interest in a genre is ''purely generic''.  When the relevant genre is regarded as an indexed family of dyadic relations, <math>G = \{ G_j \}</math>, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.

:<p><math>\textstyle \bigcup_J G = \textstyle \bigcup_j G_j = \{ (x, y) \in X \times X : (x, y) \in G_j\ (\exists j \in J) \} .</math></p>

| <math>\textstyle \bigcup_J G = \textstyle \bigcup_j G_j = \{ (x, y) \in X \times X : (x, y) \in G_j\ (\exists j \in J) \}.</math>

When the relevant genre is contemplated as a triadic relation, ''G''&nbsp;&sube;&nbsp;''J''&nbsp;&times;&nbsp;''X''&nbsp;&times;&nbsp;''X'', then one is dealing with the projection of ''G'' on the object dyad ''X''&nbsp;&times;&nbsp;''X''.

When the relevant genre is contemplated as a triadic relation, <math>G \subseteq J \times X \times X</math>, then one is dealing with the projection of <math>G\!</math> on the object dyad <math>X \times X</math>.

:<p><math>G_{XX} = proj_{XX}(G) = \{ (x, y) \in X \times X : (j, x, y) \in G\ (\exists j \in J) \} .</math></p>

| <math>G_{XX} = \operatorname{proj}_{XX}(G) = \{ (x, y) \in X \times X : (j, x, y) \in G\ (\exists j \in J) \}.</math>

On these occasions, the assertion that (''x'',&nbsp;''y'') &isin; <font size="+2">&cup;</font>_''J''&nbsp;''G'' = ''G''_''XX'' can be indicated by any one of the following equivalent expressions:

On these occasions, the assertion that (''x'',&nbsp;''y'') &isin; <font size="+2">&cup;</font>_''J''&nbsp;''G'' = ''G''_''XX'' can be indicated by any one of the following equivalent expressions: