ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Basic binary operation
Unsigned basic binary operation
Semimetric
Metric
Metric space
Definition D1400
Set distance
Formulation 1
Let $M = (X, d)$ be a D1107: Metric space such that
(i) $E, F \subseteq X$ are each a D78: Subset of $X$
The distance from $E$ to $F$ in $M$ is the D5237: Unsigned basic number \begin{equation} d(E, F) : = \inf_{x \in E, \, y \in F} d(x, y) \end{equation}
Formulation 2
Let $M = (X, d)$ be a D1107: Metric space such that
(i) $E, F \subseteq X$ are each a D78: Subset of $X$
The distance from $E$ to $F$ in $M$ is the D5237: Unsigned basic number \begin{equation} d(E, F) : = \inf \{ d(x, y) : x \in E, y \in F \} \end{equation}
Children
D1402: Closed ball