Definition:Supremum Metric/Bounded Real Sequences
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Definition
Let $A$ be the set of all bounded real sequences.
Let $d: A \times A \to \R$ be the function defined as:
- $\ds \forall \sequence {x_i}, \sequence {y_i} \in A: \map d {\sequence {x_i}, \sequence {y_i} } := \sup_{n \mathop \in \N} \size {x_n - y_n}$
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
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.2$: Examples: Example $2.2.17$