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Topic: Induction is Wrong
Replies: 8   Last Post: Nov 30, 2012 5:55 PM

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 reasterly@gmail.com Posts: 609 Registered: 9/24/07
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 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:

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

Date Subject Author
11/29/12 reasterly@gmail.com
11/29/12 J. Antonio Perez M.
11/29/12 Dan Christensen
11/30/12 quasi
11/30/12 Brian Q. Hutchings
11/30/12 Brian Q. Hutchings
11/30/12 quasi
11/30/12 Rupert
11/30/12 Brian Q. Hutchings