Sequences

In the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, let $X$ be a set.

¶ A sequence in $X$ is a map $a:\mathbb{N}\to X$. Its value $a_{n}=a(n)$ is its $n$-th term, and the sequence is written $(a_{n})_{n\in\mathbb{N}}$ or $(a_{n})$.