Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Induction is Wrong
Posted:
Nov 29, 2012 9:27 PM


Andrew Boucher has developed a theory called General Arithmetic (GA): http://www.andrewboucher.com/papers/ga.pdf
GA is a subtheory of Peano Arithmetic (PA). If we add an induction axiom (IND) to the axioms of Ring Theory (RT) then GA is also a subtheory of RT+IND. (We also need a weak successor axiom).
Boucher proves Lagrange's four square theorem, every number is the sum of four squares, is a theorem of GA. Since the four square theorem is not true in the integers, the integers can not be a model for GA, PA, or RT+IND.
GA also proves multiplication is commutative. It is well known there are noncommutative rings. There are even finite noncommutative rings: http://answers.yahoo.com/question/index?qid=20090827201012AAD7qJg
Induction is wrong. It proves multiplication, as defined by the axioms of ring theory, must be commutative when this is not true.
Russell  Integers are an illusion



