The real numbers can also be constructed from Peano's axioms. It should be possible to prove than no irrational number is equal to a natural number. Deny it if you want to look like a complete idiot, WM.
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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.