different between tuple vs relation

English

Wikibooks

Wikibooks

Etymology

From the ending of the words quintuple, sextuple; from Latin -plus.

Pronunciation

• (UK) IPA^(key): /?t?p?l/, /?t??u?p?l/, /?tju?p?l/
• (US) IPA^(key): /?tu?p?l/, /?t?p?l/
• Rhymes: -u?p?l, -?p?l

Noun

tuple (plural tuples)

1. (set theory) A finite sequence of terms.

   A tuple is not merely a totally-ordered set because the same element can appear more than once in a tuple: for example, ${\displaystyle (a,b,a)}$ qualifies as a 3-tuple whereas it would not qualify as a totally-ordered set (of cardinality 3), because the set would be ${\displaystyle \{a,b\}}$ where ${\displaystyle a\leq b}$ and ${\displaystyle b\leq a}$ so that ${\displaystyle a=b}$; i.e., it would actually be a one-element set, ${\displaystyle \{a\}}$, not even just two-element.

   If commutativity were added to a tuple, it would turn into a multiset or "bag". For example, words (of some alphabetic language) can be considered to be tuples of letters. If the ordering requirement on those letters were lifted, then the word would become a multiset of letters equivalent to those of its anagrams.

2. (computing) A single row in a relational database.
3. (computing) A set of comma-separated values passed to a program or operating system as a parameter to a function call.
4. (computing) In some programming languages, a data type that is similar to but distinct from the list data type, whose instances are characterized by having a rather fixed arity, and the elements of which instances can differ from each other by data type. (Note: this definition may overlap with the previous one.)

   Both Python and Haskell have a tuple data type as well as a list data type.

   Unlike lists, tuples are not formed by consing.

Synonyms

• (finite sequence of terms): n-tuple (when the sequence contains n terms), ordered pair (when the sequence contains exactly two terms), triple or triplet (when the sequence contains exactly three terms)

Related terms

• -tuple
• ordered pair
• tuplet
• component

Translations

Anagrams

• let up, let-up, letup, plute

English

Etymology

From Middle English relacion, relacioun, from Anglo-Norman relacioun and Old French relacion (whence French relation), from Latin rel?ti?, noun of process form from perfect passive participle rel?tus (“related”), from verb refer? (“I refer, I relate”), from prefix re- (“again”) + fer? (“I bear, I carry”).

Morphologically relate +? -ion

Pronunciation

• enPR: r?-l?'sh?n, IPA^(key): /???le???n/
• Rhymes: -e???n

Noun

relation (countable and uncountable, plural relations)

1. The manner in which two things may be associated.

   • Carried somehow, somewhither, for some reason, on these surging floods, were these travelers, of errand not wholly obvious to their fellows, yet of such sort as to call into query alike the nature of their errand and their own relations. It is easily earned repetition to state that Josephine St. Auban's was a presence not to be concealed.

2. A member of one's extended family; a relative.

3. The act of relating a story.
   • 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,^[1]

     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,^[2]

     […] 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 […]
4. (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.

5. (set theory) Specifically, a set of ordered pairs; a binary relation.

6. (databases) A set of ordered tuples retrievable by a relational database; a table.

7. (mathematics) A statement of equality of two products of generators, used in the presentation of a group.
8. (category theory) A subobject of a product of objects.
9. (usually collocated: sexual relation) The act of intercourse.

Synonyms

• (way in which two things may be associated): connection, link, relationship
• (member of one's family): relative
• (act of relating a story): recounting, telling
• (mathematics: set of ordered tuples): correspondence
• See also Thesaurus:relative

Hyponyms

• (set theory): function

Derived terms

Related terms

• relate
• relational
• relative
• relator

Translations

Anagrams

• Oriental, Tirolean, oriental, taileron, tenorial

French

Etymology

From Old French relacion, from Latin rel?ti?.

Pronunciation

• IPA^(key): /??.la.sj??/

Noun

relation f (plural relations)

1. relation
2. relationship

Further reading

• “relation” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Anagrams

• enrôlait, oriental

Swedish

Etymology

From Latin rel?ti?.

Pronunciation

• IPA^(key): /r?la??u?n/

Noun

relation c

1. relation; how two things may be associated
2. (mathematics) relation; set of ordered tuples
3. (computing) relation; retrievable by a database

Declension

See also

• samband

Anagrams

• laotiern