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Everything about Mathematical induction

Form of mathematical proof

Mathematical induction is a method for proving that a statement is true for every natural number, that is, that the infinitely many cases   all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder:Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung and that from each rung we can climb up to the next one. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Mathematical inductionA 5-minute orientation
  2. Skim a recent paper: An Improved Mathematical Model for Speed Sensorless Control of Fixed Pole Bearingless Induction MotorInfluential work since 2022
  3. Pick up a classic book: Fooled by randomnessThe most-reprinted book on the subject
  4. Read the landmark paper: Automated Mathematical InductionCited 37 times
  5. Go sideways: Peano axiomsA closely related topic
  6. Go sideways: Mathematical proofA closely related topic

📖 Definitions

Noun A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n≥0, P(n) implies P(n+1), then P(n) is true for any natural number n.

🗂️ The subject at a glance

  1. History
  2. Description
  3. Examples
  4. Variants
  5. Example of error in the induction step
  6. Formalization
  7. Transfinite induction
  8. Relationship to the well-ordering principle

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics