sequence

Sequence

A sequence is an ordered “collection” of elements with indices subset of the natural numbers.
They may be finite (→ n-tuple) or infinite.

Formally, a sequence is an indexed family with the linearly ordered index set $\{n_0,\dots ,n\}\subseteq \mathbb{N}$

$$x:\mathbb{N}\to X,n\to x_n$$

Sequences are commonly denoted as $(a_1,a_2,a_3,\dots ,a_n)$ or $(a_n{)}_{n=1}^{\infty }=(a_n{)}_{n\ge 1}=(a_k{)}_{k\in \mathbb{N}}$, or in context also $(a_n)$.
The starting index $n_0$ may vary, but is often $1$ or $0$.

Ordered $⟹$ $(a,b)\ne (b,a)$, as opposed to sets $\{a,b\}=\{b,a\}$