Category Archives: 21st Century Peano Addition Authors

Virginia Standards of Learning Math v Peano Axioms

The difficulty of the Peano Axioms is not greater either in abstraction or in formulas from algebra I.  Natural numbers are defined by the Peano Axioms below. To give away the answer, they are 0,1,2,.. Note the natural numbers are … Continue reading

Posted in Algebra One, Algebra One Word Problems, Carl Lee University of Kentucky, Edmund Landau Peano Axioms, Peano Axioms, Virginia Standards of Learning, Virginia Standards of Learning Algebra One, Virginia Standards of Learning Math | Tagged , , | Leave a comment

David Groisser Initial Segments before addition from Peano Axioms

Richard Dedekind in 1888 did order before addition.  Dedekind first did properties of closed sets under a function that is 1 to 1.   Then he applied this to tail sets under successor in effect.  Tail sets are natural numbers from … Continue reading

Posted in David Groisser, David Pierce, Head Segments of Natural Numbers, Initial Segments Groisser Style, Initial Segments of Natural Numbers, MOOC, Order First | 1 Comment

re: Alexandre Borovik Why is arithmetic difficult?

Math professor Alexandre Borovik has a post on understanding why arithmetic is difficult to learn.  It is because it has a greater conceptual structure than is realized.  He points out this complexity goes from hidden to explicit by use of … Continue reading

Posted in Addition Proofs, Alexandre Borovik, Christian Spannagel, Folge der natürlichen Zahlen, Peano Axioms for Pre-Service Teachers, PH-Heidelberg Teacher Education Math, Pre-Service Teacher Math Education, Proof and Works | Leave a comment

Milgram Russia uses implicit Peano Axioms from Grade 1

Professor R. James Milgram of the Stanford Math Department is extensively involved in math education at the elementary school level. Milgram stresses that in Russia, the elementary school math program is better devised than in the US.  The math program … Continue reading

Posted in 21st Century Peano Addition Authors, Addition Proofs, Difficult Math Problems for Grades 1 to 3, Multiplication Associative, Multiplication Commutative, Multiplication Distributive, Multiplication Proofs, Peano Axioms, Peano Axioms Implicit First Grade, Proof Addition is Associative, Proof Addition is Commutative, Recursive Inductive Definition of Multiplication, Recusive Inductive Definition of Addition, Russian Math Education, Use of x early | 1 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

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