6tuple

A 6tuple, also called a sextuple, is an ordered collection of six elements. It is typically written as (a1, a2, a3, a4, a5, a6), where each component ai comes from a specified set Ai. The 6-tuple is an element of the Cartesian product A1 × A2 × A3 × A4 × A5 × A6; the order of the components is significant, and two sextuples are equal only if every corresponding component is equal. The six components may belong to different types or domains.

Notation varies; common forms include (a1, a2, a3, a4, a5, a6) and ⟨a1, a2, a3, a4, a5, a6⟩. The term sextuple is the conventional synonym for 6-tuple.

Examples: (1, "apple", false, 2.7, "red", 42) illustrates components drawn from different domains. The set of all such six-tuples is the Cartesian product A1 × A2 × A3 × A4 × A5 × A6. If each Ai is nonempty, this product is likewise nonempty.

Applications: Six-tuples encode structured data with six fields, such as records in databases, the parameters of a six-argument function, or coordinates in a six-dimensional space in appropriate contexts. They generalize the idea of ordered n-tuples, or k-tuples, for any k, and relate to Cartesian products in set theory and mathematics.