Answer: An infinite set can be placed in bijection with a proper subset of itself, leaving room for injective maps that miss elements.
- A An infinite set can be placed in bijection with a proper subset of itself, leaving room for injective maps that miss elements
- B Infinite sets never admit one-one functions in the majority of documented cases
- C Onto functions cannot be defined on infinite sets under standard conventions
- D The pigeonhole principle applies only when the codomain is uncountable
Correct answer: A. An infinite set can be placed in bijection with a proper subset of itself, leaving room for injective maps that miss elements
Explanation: The finite argument relies on counting; with infinite sets f(n) = 2n on ℕ is injective yet misses every odd number.
Concept context
Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions