(i) | $a, b \in \mathbb{R}$ are each a D993: Real number |

**left-closed real interval**from $a$ to $b$ is the D11: Set \begin{equation} [a, b) : = \{ x \in \mathbb{R} : a \leq x < b \} \end{equation}

▾ 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

▾ Left-closed interval

▾ 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

▾ Left-closed interval

Formulation 0

Let $P = (\mathbb{R}, {<})$ be the D1101: Strictly ordered set of real numbers such that

The **left-closed real interval** from $a$ to $b$ is the D11: Set
\begin{equation}
[a, b)
: = \{ x \in \mathbb{R} : a \leq x < b \}
\end{equation}

(i) | $a, b \in \mathbb{R}$ are each a D993: Real number |