Category Archives: Mathematical Induction

Review of Introduction to Mathematical Thinking by Keith Devlin

This is a review of the book Introduction to Mathematical Thinking by Keith Devlin.  This is a paperback book of length x + 92, i.e. 102 pages.  This is a paperback that can fit into a large boxy like extra … Continue reading

Posted in Devlin Mathematical Thinking Coursera, Easy Algebra Math Induction Proofs, Keith Devlin Stanford, Mathematical Induction, Mathematical Induction BaHIC, Mathematical Thinking, MOOC, MOOCPIT | Leave a comment

Infectious zero spreads to all natural numbers

This is like saying a set of naturals closed under succession that contains zero equals all natural numbers. A set of naturals we could call a natural set. Infected zero equals all naturals. If by infected we mean also infectious … Continue reading

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Pair of Number Lines and Successor Identities

This post concerns using a pair of number lines to illustrate the successor identities.  At lower grade levels, we can simply use a pair of number lines to “prove” the successor identities.   We actually make them plausible, but at an … Continue reading

Posted in Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Lesson Plans, Lessons Lower Elementary Grade Levels, Number Line Induction, Number Line Recursion, Pair of Number Line Method of Addition, Recusive Inductive Definition of Addition, Teaching prime notation with number lines, Teaching x and y with Number Lines | 1 Comment

Re Mathematical Induction and Induction in Mathematics Lance J. Rips Jennifer Asmuth

Lance and Rips state in the conclusion to their paper on page 394: We’ve argued elsewhere (Rips, Bloomfield, & Asmuth, 2006) that math induction is central to knowledge of mathematics: It seems unlikely that people could have correct concepts of … Continue reading

Posted in Jennifer Asmuth, Lance Rips, Math Ed Psychology, Mathematical Induction, Psychological, Psychology of Mathematical Induction | 5 Comments

David Joyce Notes on Richard Dedekind’s “Was sind und was sollen die Zahlen?”

Professor David E. Joyce of Clark University has written up a very valuable set of notes on Richard Dedekind’s book, “Was sind und was sollen die Zahlen?”  (What are and should be the numbers?) (Zahlen is capitalized in German because … Continue reading

Posted in David E. Joyce, Easy Algebra Math Induction Proofs, Essays on the Theory of Numbers, Joyce Notes on Dedekind Nature of Numbers, Richard Dedekind, The Nature and Meaning of Numbers, Uncategorized, Wooster Woodruff Beman | Leave a comment

Leon Henkin On Mathematical Induction

Leon Henkin On Mathematical Induction 1960 is available for free download at Jstor. Stable Link:  http://www.jstor.org/stable/2308975 You can click on the download pdf at the above link. This article is easier in some parts than others.   As it goes on, … Continue reading

Posted in 20th Century Peano Addition Authors, 21st Century Peano Addition Authors, Edmund Landau, Inductive Definitions, Leon Henkin, Leonard Blackburn, Mathematical Induction, New Math, Recursion, Recursive Definitions, Richard Dedekind | Leave a comment

The Axiom of Proof

Mathematical Induction is not just a technique but a fundamental method of proof for the natural numbers.  The natural numbers are 0,1,2, and so on.  The axiom of induction is what handles the and so on. Axiom of Induction If … Continue reading

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