Category Archives: Richard Dedekind

Modified Dedekind Closure approach

The following is a sort of way to start this, but requires something else. ==Starting from here a possible approach to critique Consider the set of naturals that has i and j in it, that contains the successor of each … Continue reading

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#mtt2k Khan Academy videos procedural v conceptual v structural

Procedural v conceptual is highly ambiguous on the conceptual fork and even somewhat ambiguous on procedural.   If procedural is the same as recursive math or constructive math or computable math, then procedural covers most of the subject matter of algebra … Continue reading

Posted in Dedekind and Peano Academy, Euler Academy, Fictional Academies, Giuseppe Peano, Grassmann, Hermann Grassmann, Lacroix, Lagrange and Laplace Academy, Procedural v Structural math, Richard Dedekind, The Nature and Meaning of Numbers | Leave a comment

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

Richard Dedekind Essays on Numbers On-line

The Richard Dedekind book from 1888 that contains New Math in all its original glory is available in English for free. The following was typed into latex and then converted to pdf: http://www.gutenberg.org/files/21016/21016-pdf.pdf The Nature and Meaning of Numbers starts … Continue reading

Posted in Confession of Arithmetic Faith, Essays on the Theory of Numbers, Head Segments of Natural Numbers, Initial Segments of Natural Numbers, New Math Done Right, Number Line, Pair of Number Line Method of Addition, Tails of Natural Numbers, The Nature and Meaning of Numbers, Wooster Woodruff Beman | 1 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

Pre-Algebra New Math Done Right Peano Axioms

Book description: Pre-Algebra New Math Done Right is the book that 1960s era New Math should have done but didn’t.  1960s era New Math failed to focus on how we understand order and addition of natural numbers.  Richard Dedekind in … Continue reading

Posted in Giuseppe Peano, Hermann Grassmann, Mathematicians who created New Math, New Math, Richard Dedekind, Uncategorized | Leave a comment