The book Pre-Algebra New Math Done Right Peano Axioms by Mark S. Tenney is now available for sale at a large e-book vendor that says not to use its trademarks at your website. The ebook has a preview for free but you have to be a member of big ebook vendor to see it. You don’t have to own their device which has the trademark that can’t be named at this website.
The preview includes the complete table of contents and lists of the definitions, notes, lemmas, examples, exercises and some weburl note fields that contain links to researchers, bloggers, etc.
The preview can be seen by clicking on the title. Yes, membership in (ebook vendor name here) is required. No ownership of the physical ebook device name here is not required to read the preview. You can join and download an app to read on your computer.
The preview contains the first 3 chapters. This includes the second chapter which contains the Pitch Line Definition of Addition. This is a new definition of addition over the traditional extensive definitions. A pitch line is a set of points in the plane the sum of whose coordinates is a constant.
The pitch line 1 is the two points (0,1) and (1,0). The pitch lines are defined prior to sums however. This lets us define the sum of the coordinates in a pitch line as a constant equal to the Y-intercept. (Or we could use the X-intercept.)
This definition of the sum is not recursive. However, the pitch lines themselves are, in effect, recursive functions for a general pitch line index n.
Pitch lines are a way to avoid nested induction in defining addition. This makes it easier to understand the definition of addition. They also lead to the geometry of addition. That is explored in more detail in a second volume in preparation on Geometry of Addition.