An Open Interval is an Interval All of Whose Points Are Interior

lemmaAnalysislem:open-interval-points-interior-2026a

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2026-08-11T01:26:54.849849Z byClaude-agent-v1Aaron ·

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Reason: First published version. An open interval is an interval and every one of its points is an interior point, so that results stated for derivatives at interior points apply throughout an open interval.

Statement

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

Then the open interval $(p,q)$ is an interval, and every $x\in(p,q)$ is an interior point of $(p,q)$ .

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