Counterexample

Is this true?

$C^\infty$ implies analytic

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 analyticity

Go deeper· Explained in full in Analyticity, the identity theorem and zeros· Asked in CSIR NET June 2025· From Analytic Functions › Power series and analyticity

ShareWhatsApp Telegram