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Part BCSIR NET June 2024existence-vs-uniqueness

Existence vs uniqueness

What is the cardinality of the set of real solutions of eˣ + x = 1?

  1. A.0
  2. B.1✓ Correct
  3. C.Countably infinite
  4. D.Uncountable

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 existence vs uniqueness.

See pricing

50 are analysed free — try those first.

The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

Drill statements like this

Related counterexample: Continuous on a bounded interval ⇒ bounded

More on this topic

The chapter behind this: Continuity vs uniform continuity vs Lipschitz — free to read

From Continuity and Differentiation › Continuity, uniform continuity, Lipschitz

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