Skip to content
Part BCSIR NET June 2024interval-has-cardinality-of-R

Interval has cardinality of R

Let S = {x∈R:x>1x \in \mathbb{R} : x > 1 and (1−x4)/(1−x3)>22(1 - x^{4})/(1 - x^{3}) > 22}. Which of the following is true about S?

  1. A.S is empty.
  2. B.There is a bijection between S and N\mathbb{N}
  3. C.There is a bijection between S and R\mathbb{R}✓ Correct
  4. D.There is a bijection between S and a non-empty finite set

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.

See pricing

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

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram