Counterexample

Is this true?

If f is holomorphic on the domain enclosed by $\gamma$ except possibly at isolated points, and $\oint_\gamma f = 0$ , then f has no singularity inside

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

Keep practicing

Standard counterexample

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

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

complex contour integration

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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