(January 6, 2013 at 7:00 pm)Rhythm Wrote: Now I have to do your googling for you as well....
In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems.
http://en.wikipedia.org/wiki/Axiom
http://en.wikipedia.org/wiki/Peano_axioms
Perhaps these links will help you to understand why 1+1=2 is not an axiom (since my summarizing it in a few sentences posts ago did not).
we are at an impasse and before we continue I think we need more opinion so I will wait to see what others say on this.