[Term] Mathematical Induction

• Mathematical Induction is a special method proofing or proof technique. It is used to prove statements about all natural numbers.
• Mathematical Induction

  Steps:

  • Base Case
  • Inductive Step
• Step 1: Base Case: Show that P(1) is true.
• Step 2: Inductive Step: Assume that P(k) is true for an arbitrary positive integer k (it is called the Inductive Hypothesis). Then, show that P(k+1) must also be true. POLYTECHNIC UNIVERSITY OF THE P
• Simplified Instructions:

  • Let n = k.
  • Double the term before the equal sign.
  • Substitute k by k + 1 (except the second to the last term before equal sign).
  • Replace the original left-side statement (except the term before the equal sign) with the original right-side statement (on the first step which is let n = k).
  • Prove that both sides are equal.