Entry 24: Mathematical Induction - The Domino Promise
Mathivation Research Lab Notebook Entry 24: Mathematical Induction - The Domino Promise Opening Thought "Truth becomes powerful when it can continue forever." Suppose a visitor comes to Mumbai in July. It rains. He visits again the next July. Again it rains. Five years later... Still raining. He smiles and says, "It always rains in Mumbai in July." The class smiles. Teacher: "Is that a proof... or just a strong pattern?" Silence. Patterns are beautiful. Proofs are stronger. Mathematics teaches us the difference. Today we explore one of the most elegant proof techniques in mathematics... Mathematical Induction. Lab Observation The whiteboard had a long row of dominoes drawn across it. The teacher gently pointed towards the first domino. Teacher: "If I push only the first domino, will all of them fall?" Some learners nodded. Some looked doubtful. One learner quickly replied, "Only if every domino is close enough...