Counterexample

Is this true?

Continuous on a bounded interval ⇒ bounded

No — it is false.

The counterexample

f(x) = 1/x on (0,1)

Why it fails

Needs a compact (closed) domain.

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Keep practicing

Pointwise vs uniform

The mode of convergence — or of continuity — was the wrong one.

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Continuity vs uniform continuity vs Lipschitz· Asked in CSIR NET December 2025· From Continuity and Differentiation › Continuity, uniform continuity, Lipschitz

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.

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