On Thursday, 20 March 2014 20:51:31 UTC+1, Dan Christensen wrote: > In formal proofs, your > axioms are your entire world. You cannot use any other "facts" no matter how > "obvious" they might be.
Then let us know whether pi is a natural number - from the Peano axioms which, according to you, "fully capture the common intuition of the natural numbers". Do not use any other "facts". And don't answer that we have not yet pi. I have it, and many other readers of the Peano axioms have it too.