Sequences

Definition: Sequence

A sequence is a function whose domain is an interval of integers.

Definition: Finite Sequence

A sequence is finite iff its domain is finite.

Definition: Infinite Sequence

A sequence is infinite iff its domain is not finite.

NOTATION

The notation used for sequences is a bit different than the typical notation used for functions.

Let $f:D\to X$ be a sequence. Instead of writing $f:D\to X$, we usually say that $f$ is a sequence of points in $X$ and write $(x_k{)}_{k\in D}$ instead of $f$. Given a specific $d\in D$, we write $x_d$ instead of $f(d)$.