The

**set of Cauchy sequences**in $M$ is the D11: Set \begin{equation} \{ x : \mathbb{N} \to X \mid x \text{ is Cauchy in } M \} \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

▾ Cauchy sequence

▾ 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

▾ Cauchy sequence

Formulation 0

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

The**set of Cauchy sequences** in $M$ is the D11: Set
\begin{equation}
\{ x : \mathbb{N} \to X \mid x \text{ is Cauchy in } M \}
\end{equation}

The