Relation Theory • Definition

It is convenient to begin with the definition of a -place relation, where is a positive integer.

Definition.  A -place relation over the nonempty sets is
a -tuple where is a subset of the cartesian product

Several items of terminology are useful in discussing relations.

• The sets are called the domains of the relation with being the domain.

• If all the are the same set then is more simply described as a
  -place relation over

• The set is called the graph of the relation on analogy with the graph of a function.

• If the sequence of sets is constant throughout a given discussion or is otherwise determinate in context then the relation is determined by its graph making it acceptable to denote the relation by referring to its graph.

• Other synonyms for the adjective -place are -adic and -ary, all of which leads to the integer being called the dimension, adicity, or arity of the relation

Resources

• Sign Relations
• Triadic Relations
• Survey of Relation Theory
• Peirce’s 1870 Logic Of Relatives

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