Finite Sequence

Definition

Finite Sequence

A finite sequence of length $n\ge 0$ in a set $A$, where $n$ is an integer, is a function

$$a:\{1,\dots ,n\}\to A,i\mapsto a_i,$$

written $(a_1,\dots ,a_n)$. The index $i$ specifies a position, and $a_i$ is the term at that position. Order matters, and terms may repeat.

Unlike an infinite sequence, it has only finitely many positions.