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
Closed real interval
Definition D543
Open real interval
Formulation 0
Let $P = (\mathbb{R}, {<})$ be the D1101: Strictly ordered set of real numbers such that
(i) $a, b \in \mathbb{R}$ are each a D993: Real number
The open real interval from $a$ to $b$ is the D11: Set \begin{equation} (a, b) : = \{ x \in \mathbb{R} : a < x < b \} \end{equation}
Formulation 1
Let $P = (\mathbb{R}, {<})$ be the D1101: Strictly ordered set of real numbers such that
(i) $a, b \in \mathbb{R}$ are each a D993: Real number
The open real interval from $a$ to $b$ is the D11: Set \begin{equation} (a, b) : = \{ x \in \mathbb{R} : a < x, x < b \} \end{equation}
Children
Open real unit interval