Category Archives: Addition Definitions

Counting on Definition of Addition

We define counting on by one and give it the special prime symbol. 1=0′ 2=1′ We define addition by two rules for counting on. Counting on by zero rule n+0 = n Counting on by one more rule m+n’ = … Continue reading

Posted in Addition as counting, Addition Definitions, Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Counting on Definition of Addition | Leave a comment

Re Steve Wasserman The Nation The Amazon Effect

Steve Wasserman at The Nation writes about the impact of Amazon on publishing and book selling. The Amazon Effect The article is mostly negative on Amazon.  Some of the comments present a pro-Amazon view.  This provides some needed balance. The … Continue reading

Posted in e-book market, Kalmar Definition of Addition, Pitch Line Definition of Addition, Publishing | Tagged , , | 1 Comment

Keith Devlin Transition to College Math MOOC

Keith Devlin of Stanford University will have a MOOC course on transition to college math.  This will not be a full course, but a partial course.  He is hoping to get schools to use it as part of their courses.  … Continue reading

Posted in Addition Left Identities, Addition Left Successor Identity, Addition Left Zero Identity, Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Edmund Landau, Geometry of Addition, Kalmar Definition of Addition, Keith Devlin Stanford, Laszlo Kalmar, MOOC, Pitch Line Addition, Transition to College Math | Leave a comment

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

Is addition just counting?

Suppose you are given two sets.  One contains 2 items and the other 3.  You form a single set and count them 1 to 5.  This is addition.  What is wrong with this? Addition from Peano Axioms is consistent with … Continue reading

Posted in Addition as counting, Addition Definitions, Iterated Succession, Number Line, Pair of Number Line Method of Addition, Repeated Succession, Set theory definition of addition | 15 Comments