Counterexample

Is this true?

Pointwise limit of continuous functions is continuous

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

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

uniform convergence

Go deeper· Explained in full in Uniform convergence — what it buys and how to test it· Asked in CSIR NET December 2025· From Sequences and Series of Functions › Pointwise vs uniform convergence, M-test, Dini

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