(i) | $E, F \subseteq X$ are each a D78: Subset of $X$ |

**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}

▾ 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

▾ 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

Formulation 1

Let $M = (X, d)$ be a D1107: Metric space such that

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}

(i) | $E, F \subseteq X$ are each a D78: Subset of $X$ |

Formulation 2

Let $M = (X, d)$ be a D1107: Metric space such that

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}

(i) | $E, F \subseteq X$ are each a D78: Subset of $X$ |

Child definitions