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→Definition: bind expressions
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The formal definition of a '''finite arity relation''', specifically, a '''k-ary relation''' can now be stated.
The formal definition of a '''finite arity relation''', specifically, a '''k-ary relation''' can now be stated.
−* '''Definition.''' A '''k-ary relation''' ''L'' over the nonempty sets ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub> is a (1+''k'')-tuple ''L'' = (''F''(''L''), ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub>) where ''F''(''L'') is a subset of the cartesian product ''X''<sub>1</sub> × … × ''X''<sub>''k''</sub>. If all of the ''X''<sub>''j''</sub> for ''j'' = 1 to ''k'' are the same set ''X'', then ''L'' is more simply called a '''''k''-ary relation over ''X'''''. The set ''F''(''L'') is called the ''figure'' of ''L'' and, providing that the sequence of sets ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub> is fixed throughout a given discussion or determinate in context, one may regard the relation ''L'' as being determined by its figure ''F''(''L'').
+* '''Definition.''' A '''k-ary relation''' ''L'' over the nonempty sets ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub> is a (1+''k'')-tuple ''L'' = (''F''(''L''), ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub>) where ''F''(''L'') is a subset of the cartesian product ''X''<sub>1</sub> × … × ''X''<sub>''k''</sub>. If all of the ''X''<sub>''j''</sub> for ''j'' = 1 to ''k'' are the same set ''X'', then ''L'' is more simply called a '''''k''-ary relation over ''X'''''. The set ''F''(''L'') is called the ''figure'' of ''L'' and, provided that the sequence of sets ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub> is fixed throughout a given discussion or is otherwise determinate in context, one may regard the relation ''L'' as being determined by its figure ''F''(''L'').
−The formal definition simply repeats more concisely what was said above, merely unwrapping the conceptual packaging of the relation's ground to define the relation in 1 + ''k'' parts, as ''L'' = (''F''(''X''), ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub>), rather than just the two, as ''L'' = (''F''(''L''), ''G''(''L'')).
+The formal definition simply repeats more concisely what was said above, merely unwrapping the conceptual packaging of the relation's ground to define the relation in 1 + ''k'' parts, as ''L'' = (''F''(''X''), ''X''<sub>1</sub>, …, ''X''<sub>''k''</sub>), rather than just the two, as ''L'' = (''F''(''L''), ''G''(''L'')).
A ''k''-ary '''predicate''' is a ''[[boolean-valued function]]'' on ''k'' variables.
A ''k''-ary '''predicate''' is a ''[[boolean-valued function]]'' on ''k'' variables.