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Part BCSIR NET June 2024cantor-no-set-of-that-size

Cantor no set of that size

Let C be the collection of all sets S such that the power set of S is countably infinite. Which of the following statements is true?

  1. A.There exists a non-empty finite set in C
  2. B.There exists a countably infinite set in C
  3. C.There exists an uncountable set in C
  4. D.C is empty✓ Correct

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, and why this one tests standard counterexample.

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50 are analysed free — try those first.

The trap it tests

Standard counterexample

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

Drill statements like this

Related counterexample: Every ordered field is Archimedean

More on this topic

The chapter behind this: The real line: supremum, Archimedes and density — free to read

From The Real Line › Completeness, sup/inf, Archimedean property

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