Part CCSIR NET June 2024level-sets-are-discrete-but-f-may-not-vanish

Level sets are discrete but f may not vanish

Let f be an entire function such that for every integer k ≥ 1 there is an infinite set X_k such that f(z) = 1/k for all z ∈ X_k. Which of the following statements are necessarily true?

A.There exists an infinite set X such that f(z) = 0 for all z ∈ X
B.There exists a non-empty closed set X such that f(z) = 0 for all z ∈ X
C.The set X_k is unbounded for each k ≥ 1✓
D.If there exists a bounded sequence (z_k)_(k≥1) such that z_k ∈ X_k for each k ≥ 1, then f has a zero✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Level sets are discrete but f may not vanish

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