Indexed family
Undergraduate
Consider an index set $I$ and a set of values. An indexed family is a function $i \mapsto x_i$ from $I$ to the set, written \((x_i)_{i \in I}\). Unlike a set, an indexed family can repeat elements. A sequence is an indexed family with $I = \nats$.
Examples
Examples
- $(1, 2, 2)$ High school
Distinctions involving this term
- Types of collections: Mathematics has several kinds of “a bunch of things,” which differ in whether order and repetition matter. A set ignores order and repetition. A multiset keeps repetition. A sequence keeps order and repetition. “Collection” is informal, and “group” is a technical term for a set with an operation.