A Tuple is a Finite Sequence of Fixed Sequence Length..
- AKA: Tuple Point, N-Tuple.
- Context:
- Example(s):
- (0.9, RED), a 2-Tuple.
- (S, f), a 2-Tuple (e.g. representing a Multiset).
- (0.9, RED, π), a 3-Tuple.
- (0.1, π, 1.1), a Vector.
- {A/6, B/11, C+/20, ..., F/2}, marks reported for an course exam.
- (D, d) is a 2-Tuple representing a Metric Space.
- ... is a 3-Tuple representing an RDF Relation.
- (N, Σ, P, S) is a 4-Tuple representing a Formal Grammar.
- Counter-Example(s):
- {1.3, Red, 7.5}, is a Set.
- {1.3, Red, 7.5, Red}, is a Multiset.
- {1.3, 4.5, 7.5}, is a Numerical Set.
- (1,2,3,4...), is a Numerical Sequence.
- (This was a sentence .), is a String.
- (This, was, a), is a 3-gram.
- See: Tuple Space, Finite Sequence, Multiset, Abstract Space, Data Record.
References
2009
- (Wikipedia, 2009) http://en.wikipedia.org/wiki/Tuple
- In mathematics, a tuple is a sequence (also known as an "ordered list") of a specific number of values, called the components of the tuple. These components can be any kind of mathematical objects, where each component of a tuple is a value of a specified type. A tuple containing n components is known as an "n-tuple". For example, the 4-tuple (or "quadruple"), with components of respective types PERSON, DAY, MONTH and YEAR, could be used to record that a certain person was born on a certain day of a certain month of a certain year.
- Tuples are used to describe mathematical objects that consist of specified components. For example, a directed graph is defined as a tuple (V, E) where V is the set of nodes and E is a subset of V × V that denotes the edges. The type of the first object is "set of nodes" and the type of the second is "set of edges".
- In type theory, tuples are associated with product types.
- The main properties that distinguish a tuple from, for example, a set are that
- 1. it can contain an object more than once;
- 2. the objects appear in a certain order;
- 3. it has finite size.
- Note that (1) distinguishes it from an ordered set and that (2) distinguishes it from a multiset. This is often formalized by giving the following rule for the identity of two n-tuples:
- (a1, a2, …,an) = (b1, b2, …, bn) ↔ a1 = b1, a2 = b2, …, an = bn.
- Since a n-tuple is indexed by the numbers 1…n (or 0…n-1), it can be regarded as a function from a subset of ℕ:
- (a1, a2, …,an) ≡ fa: ℕn → A: i ↦ ai.
1996
1998