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Discrete Mathematics & Math
Q81 / 100
What is the Axiom of Choice and its significance?
Correct! Well done.
Incorrect.
The correct answer is B) A set-theory axiom stating that given any collection of non-empty sets, there exists a choice function selecting one element from each set — equivalent to Zorn's Lemma and Well-Ordering
B
Correct Answer
A set-theory axiom stating that given any collection of non-empty sets, there exists a choice function selecting one element from each set — equivalent to Zorn's Lemma and Well-Ordering
Explanation
AC (Cohen 1963): independent of ZF — cannot be proved or disproved from other set theory axioms. Implies Banach-Tarski paradox (sphere decomposition). Most mathematicians accept it. Constructivists reject it.
Progress
81/100