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Counterexample

Is this true?

Riemann integrable ⇒ continuous almost everywhere fails for… (i.e. 'bounded ⇒ integrable')

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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86 counterexamples are free — including most of the ones Part C leans on hardest.

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Converse assumed

The theorem runs one way. You used it in the other.

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integration

Go deeper· Explained in full in Riemann integrability — the criterion and the zoo· Asked in CSIR NET December 2025· From Integration › Riemann integration and criteria

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