relation

Etymology

From Middle English relacion, relacioun, from Anglo-Norman relacioun and Old French relacion (whence French relation), from Latin relātiō, noun of process form from perfect passive participle relātus (“related”), from verb referō (“I refer, I relate”), from prefix re- (“again”) + ferō (“I bear, I carry”). Morphologically relate + -ion

noun

1. The manner in which two things may be associated.
   The relation between diet and health is complex.
2. A member of one's extended family; a relative.
   Yes, he's a relation of mine, but only a distant one.
3. (chiefly in the plural) A relationship; the manner in which and tone with which people or states, etc. interact.
   the foreign relations of the United States
4. The act of relating a story.
   Your relation of the events is different from mine.
   1669, Letter from Dr. Merrett to Thomas Browne, in Simon Wilkin (ed.), Sir Thomas Browne’s Works including his Life and Correspondence, London: William Pickering, 1836, Volume I, p. 443, Many of the lupus piscis I have seen, and have bin informed by the king’s fishmonger they are taken on our coast, but was not satisfied for some reasons of his relation soe as to enter it into my Pinax […]
   1691, Arthur Gorges (translator), The Wisdom of the Ancients by Francis Bacon (1609), London, Preface, […] seeing they are diversly related by Writers that lived near about one and the self-same time, we may easily perceive that they were common things, derived from precedent Memorials; and that they became various, by reason of the divers Ornaments bestowed on them by particular Relations […]
   Jones […] was easily prevailed on to satisfy Mr Dowling's curiosity, by relating the history of his birth and education, which he did, like Othello. […] Mr Dowling was indeed very greatly affected with this relation; for he had not divested himself of humanity by being an attorney. 1749, Henry Fielding, Tom Jones
5. (set theory) A set of ordered tuples.
   […]Signs are, first of all, physical things: for example, chalk marks on a blackboard, pencil or ink marks on paper, sound waves produced in a human throat. According to Reichenbach, "What makes them signs is the intermediary position they occupy between an object and a sign user, i.e., a person." For a sign to be a sign, or to function as such, it is necessary that the person take account of the object it designates. Thus, anything in nature may or may not be a sign, depending on a person's attitude toward it. A physical thing is a sign when it appears as a substitute for, or representation of, the object for which it stands with respect to the sign user. The three-place relation between sign, object, and sign user is called the sign relation or relation of denotation. 1974, Thomas S. Szasz, M.D., chapter 7, in The Myth of Mental Illness, page 107
6. (set theory) Specifically, a set of ordered pairs; a binary relation.
   Equality is a symmetric relation, while divisibility is not.
7. (databases) A set of ordered tuples retrievable by a relational database; a table.
   This relation uses the customer's social security number as a key.
8. (mathematics) A statement of equality of two products of generators, used in the presentation of a group.
9. (category theory) A subobject of a product of objects.
10. (usually collocated: sexual relation) The act of intercourse.