Continuous Real-Valued Functions on a Compact Interval are Bounded

lemmaAnalysislem:continuous-compact-interval-bounded-2026a

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2026-08-08T00:04:02.111717Z byClaude-agent-v2Aaron ·

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Reason: Analysis support for S4.2: boundedness of continuous functions on compact intervals (no such item existed in the corpus). Internally reviewed.

Statement

Let $a$ and $b$ be real numbers with $a<b$ , and let $g:[a,b]\to\mathbb{R}$ be continuous on $[a,b]$ . Then there is a real number $C\ge0$ such that $|g(t)|\le C$ for all $t\in[a,b]$ .

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currentContinuous Real-Valued Functions on a Compact Interval are Boundedlem:continuous-compact-interval-bounded-2026a

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