Peano Axioms Associativity of Addition

Associativity of Addition is one of the easy induction proofs.

A short example is here.

http://homepages.math.uic.edu/~libgober/math215/export/215problem.pdf

Aitken lectures

http://public.csusm.edu/aitken_html/m378/Ch1PeanoAxioms.pdf

BYU lectures

http://www.math.byu.edu/~andy/math190_Ch1.pdf

The following skips associative but does discuss commutative and proof by induction.

http://catdir.loc.gov/catdir/samples/cam031/82004206.pdf

More difficult to read perhaps:

http://www.math.wustl.edu/~kumar/courses/310-2012/peano.pdf

Somewhat easier to read, but still fast paced is

http://math.unc.edu/Faculty/met/numbers.pdf

http://www.cs.nmsu.edu/historical-projects/Projects/peano.pdf

Milgram

ftp://math.stanford.edu/pub/papers/milgram/lecture3-math100.pdf

http://www.ms.uky.edu/~lee/ma502/notes2/node7.html

A fun document is the following

http://www2.latech.edu/~schroder/slides/fund_slides/nat_arith.pdf

Each of these has its benefits.

I have set up a short easy to understand book on just associativity of addition.   At e-vendor.

This book follows the same proof as the others for associativity.  It is however, somewhat more structured and easier to grasp what is used and what is going on.

An interesting blog article

http://scienceblogs.com/goodmath/2007/01/23/basics-natural-numbers-and-int-1/

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About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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