Infinite Sequence

Definition

Infinite Sequence

An infinite sequence in a set $A$ is a function

$$a:{\mathbb{N}}_{>0}\to A,n\mapsto a_n,$$

written $(a_n{)}_{n\ge 1}=(a_1,a_2,a_3,\dots )$. The index $n$ specifies a position, and $a_n$ is the term at that position. Order matters, and terms may repeat: infinitely many positions need not contain infinitely many distinct values.

Unlike a finite sequence, it has no final position.