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
▼ Binary endorelation
▼ Preordering relation
▼ Partial ordering relation
▼ Partially ordered set
▼ Closed interval
Definition D544
Closed real interval
Formulation 0
Let $P = (\mathbb{R}, {\leq})$ be the D1102: Ordered set of real numbers such that
(i) $a, b \in \mathbb{R}$ are each a D993: Real number
The closed real interval from $a$ to $b$ is the D11: Set \begin{equation} [a, b] : = \{ x \in \mathbb{R} : a \leq x \leq b \} \end{equation}
Formulation 1
Let $P = (\mathbb{R}, {\leq})$ be the D1102: Ordered set of real numbers such that
(i) $a, b \in \mathbb{R}$ are each a D993: Real number
The closed real interval from $a$ to $b$ is the D11: Set \begin{equation} [a, b] : = \{ x \in \mathbb{R} : a \leq x, x \leq b \} \end{equation}
Children
▶ D1510: Closed real unit interval
▶ D543: Open real interval