Answer: invalid.
- A invalid
- B still valid
- C partly valid
- D unnecessary
Correct answer: A. invalid
Explanation: Without a true base case the chain never starts, so the proof is invalid.
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.