2-Tuple

A 2-Tuple is a Tuple with 2 Members.

• AKA: Ordered Pair, Pair, Ordered 2-Tuple.
• Context:
  • It can be represented as <x,y> (or as the Ordered Set {x, {y}}).
• Example(s):
  • A Multiset, composed of a Set and a Frequency Function.
  • A Metric Space, composed of a Point Set and a Distance Function.
  • E.g. (10,Clubs) a Symbol on a Card from a Card Draw Experiment.
• See: 1-Tuple, 3-Tuple, 4-Tuple.

References

• http://www.isi.edu/~hobbs/bgt-sequences.text
  • The distinguishing feature of ordered pairs, or simply "pairs", is that they have a first and a second element.
    • (1) (forall (p) (if (pair p) (exists (x y) (and (first x p)(second y p)))))
  • We could define pairs in the traditional way in set theoretic terms. The pair <x,y> is defined as the set {x, {y}}. This is certainly a model of the axioms involving "pair", but it would be pedantic to call this the definition.