Unary Relation

A Unary Relation is a finitary relation that requires one relation argument.

• Context:
  • It can be:
    • a Unary Number Relation.
    • a Unary Set Relation.
    • a Unary Tuple Relation.
    • a Unary Vector Relation.
• Example(s):
  • Positive Number Relation(x) ⇒ True If [math]\displaystyle{ x }[/math] > 0; False otherwise.
  • Homonymy Relation(Word(x)) ⇒ Concept Set.
  • …
• Counter-Example(s):
  • a Binary Relation.
  • an n-Ary Relation.
• See: Unary Function, Unary Operation.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Relation_(mathematics)
  • In mathematics, especially set theory, and logic, a relation is a property that assigns truth values to combinations (k-tuples) of k individuals. ...
  • Since there is only one 0-tuple, the so-called empty tuple, there are only two zero-place relations, one for the property "is a 0-tuple", and one for its negation ("is not a 0-tuple"). One-place relations are called unary relations. For instance, any set (such as the collection of Nobel laureates) can be viewed as a collection of individuals having some property (such as that of having been awarded the Nobel prize). Two-place relations are called binary relations or dyadic relations. The latter term has historic priority. Binary relations are very common, given the ubiquity of relations such as: Equality and inequality, divisor of, and set membership.

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