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Induction is Wrong
Posted:
Nov 29, 2012 9:27 PM
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Andrew Boucher has developed a theory called General Arithmetic (GA):
http://www.andrewboucher.com/papers/ga.pdf
GA is a sub-theory of Peano Arithmetic (PA).
If we add an induction axiom (IND) to the axioms of Ring Theory (RT)
then
GA is also a sub-theory 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 non-commutative rings.
There are even finite non-commutative 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
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