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📐 Mathematics  ·  Principle of Mathematical Induction  ·  JEE

The principle of mathematical induction is used to prove statements for which set of numbers?

Answer: All natural numbers.

  • A All real numbers
  • B All natural numbers
  • C All irrational numbers
  • D All negative integers

Correct answer: B. All natural numbers

Explanation: Mathematical induction proves a statement P(n) holds for every natural number n, starting from a base case.

Induction as a Domino ChainP(1): base case fallsP(k) knocks down P(k+1)...and so on, foreverBase case = first domino tipped; inductive step = each domino guaranteed to tip the next one

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.

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