2-Tuple

A 2-Tuple is a tuple with 2 Members.

• AKA: Ordered Pair, Ordered 2-Tuple.
• Context:
  • It can be represented as <x,y> (or as the ordered set {x, {y}}).
  • It can be captured in a 2-Tuple Record.
  • …
• 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.

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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.

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