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Part BCSIR NET June 2023cardinal-arithmetic

Cardinal arithmetic

Suppose S is an infinite set. Assuming that the axiom of choice holds, which of the following is true?

  1. A.S is in bijection with the set of rational numbers.
  2. B.S is in bijection with the set of real numbers.
  3. C.S is in bijection with S × S.✓ Correct
  4. D.S is in bijection with the power set of S.

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 finite-dimensional intuition.

See pricing

50 are analysed free — try those first.

The trap it tests

Finite-dimensional intuition

Something true in ℝⁿ, or in a nice space, assumed in general.

Drill statements like this

Related counterexample: A subset of ℝ with measure zero is countable

More on this topic

The chapter behind this: Lebesgue measure and measurable functions — free to read

From Lebesgue Measure and Integration › Measurable sets and functions

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