Intermediate
Discrete Mathematics & Math
Q52 / 100
What is the Principle of Mathematical Induction and Well-Ordering?
Correct! Well done.
Incorrect.
The correct answer is B) Both are equivalent: induction is based on the well-ordering principle (every non-empty subset of ℕ has a minimum element), and each implies the other over ℕ
B
Correct Answer
Both are equivalent: induction is based on the well-ordering principle (every non-empty subset of ℕ has a minimum element), and each implies the other over ℕ
Explanation
Well-ordering principle: every non-empty set of natural numbers has a least element. This is equivalent to (strong) mathematical induction. Both are axioms of ℕ, each derivable from the other.
Progress
52/100