Open real interval – TheoremDex

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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}

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