Answer: Induction proves a statement for all n from the base case onward by chaining the inductive step infinitely.
- A Induction can prove a statement for just one specific value of n, leaving every other value of n unverified
- B Induction proves a statement for all n from the base case onward by chaining the inductive step infinitely
- C Induction requires checking each natural number individually by hand, one at a time, indefinitely
- D Induction works mainly for inequality statements, rarely for equalities between expressions
Correct answer: B. Induction proves a statement for all n from the base case onward by chaining the inductive step infinitely
Explanation: Induction's power is that the inductive step, once proven for arbitrary k, applies repeatedly: P(1) implies P(2), which implies P(3), and so on for every n from the base case 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.