Seventuples
A seventuple, also called a seven-tuple or septuple, is an ordered collection of seven elements. In formal terms, it is a 7-tuple (a1, a2, a3, a4, a5, a6, a7) where each component ai comes from a specified set or type. When all components come from the same set A, the set of all such seven-tuples is the seventh Cartesian power A × A × A × A × A × A × A, often denoted A^7.
- Order matters: (a1, a2, a3, a4, a5, a6, a7) is different from any other arrangement of the
- If the seven elements come from different sets A1, A2, ..., A7, then the seventuple belongs to
- Projections: there are projection functions πi that select the i-th component, returning ai.
- Nested representation: due to associativity of the Cartesian product, a seven-tuple can be viewed as nested
- If each Ai is finite with size |Ai|, the number of possible seven-tuples in A1 × A2
- Seven-tuples are foundational in areas such as databases, programming, and mathematics, where fixed-length records and ordered
- Example: (2, red, 3.14, 7, true, "xi", 0) is a seven-tuple with diverse element types.
- Applications include representing fixed-length records in data schemas, coordinates in seven-dimensional space, and function outputs that
- An n-tuple is a general term for any fixed-length ordered collection; seven is the specific case
- Septuple or seven-tuple terminology may be used interchangeably, though seven-tuple is widely understood.