Definition:Supremum Metric/Bounded Real Sequences

Definition
Let $A$ be the set of all bounded real sequences.

Let $d: A \times A \to \R$ be the function defined as:
 * $\displaystyle \forall \left\langle{x_i}\right\rangle, \left\langle{y_i}\right\rangle \in A: d \left({\left\langle{x_i}\right\rangle, \left\langle{y_i}\right\rangle}\right) := \sup_{n \mathop \in \N} \left\vert{x_n - y_n}\right\vert$

where $\sup$ denotes the supremum.

$d$ is known as the supremum metric on $A$.

Also known as
This metric is also known as the sup metric or the uniform metric.

Also see

 * Supremum Metric on Bounded Real Sequences is Metric