Answer: base case.
- A base case
- B inductive step
- C final conclusion
- D mere guess
Correct answer: A. base case
Explanation: The base case checks that the statement holds for the starting value.
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.