Intermediate
Discrete Mathematics & Math
Q57 / 100
What is Zorn's Lemma?
Correct! Well done.
Incorrect.
The correct answer is B) If every chain in a non-empty partially ordered set has an upper bound, then the set contains a maximal element — equivalent to Axiom of Choice
B
Correct Answer
If every chain in a non-empty partially ordered set has an upper bound, then the set contains a maximal element — equivalent to Axiom of Choice
Explanation
Zorn's Lemma is equivalent to the Axiom of Choice (and Well-Ordering Theorem). Used to prove: every vector space has a basis, every ring has a maximal ideal, Tychonoff's theorem. Controversial but indispensable.
Progress
57/100