Answer: all naturals from the base up.
- A all naturals from the base up
- B only for the value n = 1
- C only the even numbers involved
- D for essentially no numbers
Correct answer: A. all naturals from the base up
Explanation: Once both steps hold, P(n) is true for every natural number from the base value onward.
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.