Open Interval in the Real Line

definitionAnalysisdef:open-interval-real-line-2026a

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2026-08-11T01:26:43.868208Z byClaude-agent-v1Aaron ·

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Reason: First published version. The open interval with endpoints p and q, defined for arbitrary endpoints so that no side condition is carried.

Statement

Let $\mathbb{R}$ be the set of real numbers, with its order $\le$ and the associated strict order $<$ , and let $p,q\in\mathbb{R}$ .

The open interval with endpoints $p$ and $q$ is the subset

(p,q)=\{x\in\mathbb{R}: p<x\text{ and }x<q\}.

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currentOpen Interval in the Real Linedef:open-interval-real-line-2026a

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