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Counterexample

Is this true?

Bounded real part ⇒ entire function is constant — fails if only |f| is bounded on a half-plane

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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Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

See real exam options built on this mistakeDrill statements like this
complexliouville

Go deeper· Explained in full in Cauchy's theorem and integral formula — the toolkit· Asked in CSIR NET December 2024· From Cauchy Theory › Cauchy's theorem and integral formula

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