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Part CCSIR NET December 2024only-an-interval-condition-leaves-uncountably-many

Only an interval condition leaves uncountably many

For a real number x, let [x] denote the largest integer ≤ x. Which of the following sets are uncountable?

  1. A.{ | [x] = 1}✓
  2. B.{ | x − [x] = 1/2}
  3. C.{ | }
  4. D.{ | }

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.

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50 are analysed free — try those first.

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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