Pre-Algebra New Math Done Right Geometry of Addition Associative Law

This is 40 pages of text in one format, 28 pages after front matter. This was not processed from a pdf but is native html that is uploaded to the ebook processor. There are 346 location points in the ebook previwer.

This is the Commutative Law of Addition part of the Geometry of Addition set. This is part nine of Geometry of Addition.

Pre-Algebra New Math Done Right Geometry of Addition

This is a continuation from:

Pre-Algebra New Math Done Right Peano Axioms

This book is on the geometry of Peano Axiom addition. This book contains a new definition of addition in the Peano Axiom framework. This is called pitch line addition. Let x' = x+1 and 'y = y-1. The new definition is

x+0 = x

x' + 'y = x+y

Lines of constant x+y are defined prior to defining addition. These are called pitch lines. Their properties are proven. This is new material to math.

The book contains no pdf, jpeg, or pngs. It is pure html.

Entire book is approximately 240 pages of material when formatted as a pdf. The entire book contains a total of 270 exercises, 119 lemmas, 30 note fields, 6 web url note fields, 161 examples, and 54 definitions. This is a total of 640 fields. This is in addition to the text. It is organized into 33 chapters. Fields and chapters are renumbered within each part of the overall work.

The first volume Peano Axioms has 178 Examples, 463 Exercises, 98 definitions, 45 Lemmas with proofs, references to over 96 web pages, 58 chapters, and is 391 pages when formatted as pdf with Latex. 178 examples + 463 exercises + 98 definitions + 45 lemmas + 96 webpages equals 880. Added to the 640 fields above is 1520 fields. This is in addition to the text not in such fields.

Total examples is 178 + 161 = 339 examples. 463 + 270 = 733 Exercises. 54 + 98 = 152 definitions. 119+45 = 164 lemmas. 96+6 = 102 web page references. 58+33 = 91 chapters. 391 + 240 = 631 pages.

There are no quadratic or higher algebra formulas. Students complain about complicated algebra in learning how to do proofs by mathematical induction. This material is thus the ideal for learning mathematical induction proofs.

These totals compare to treatments of 20 pages on university web pages on the Peano Axioms and Peano Addition. Some may contain more, but usually these go beyond just the Peano Axioms and Peano Addition. Those mostly are repeats of each other. Those tend to be theoretical and without starter examples and starter exercises. They also tend to duplicate each other. Thus in terms of distinct and unique material on the Peano Axioms and Peano Addition, the bulk of it is apparently contained in these materials.


The book is divided into ten parts. These are not of equal length. The pricing approximately reflects the length of each part. So short parts are priced at the minimum allowed. Overall the sum of the prices of the parts is fair for the sum of the lengths.

Ten parts of book

Geometry of Addition Introduction

Addition bead shift definition and diagrams

Pitch line drills

Addition geometry fundamentals

Lattice square induction

Pitch line lemmas

Y-intercept function

Pitch Line induction

Addition Commutative

Addition Associative

Keywords

Peano Axioms, Addition Geometry, Pitch Line Addition, Mathematical Induction, Recursion, Transition to Proof, Mathematical Thinking