Definitions
,
Results
,
Conjectures
▾
Set of symbols
▾
Alphabet
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Deduction system
▾
Theory
▾
Zermelo-Fraenkel set theory
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Set
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Binary cartesian set product
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Binary relation
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Map
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Operation
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N-operation
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Binary operation
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Basic binary operation
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Unsigned basic binary operation
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Semimetric
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Metric
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Metric space
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}
Child definitions
»
D1402: Closed ball
