On Mon, 11 Apr 2011 15:55:37 -0700, geremy condra wrote:
>> Ah, I didn't know that! How wonderful! But in any case, Presburger >> arithmetic is much weaker than even Peano arithmetic. >> >> http://en.wikipedia.org/wiki/Presburger_arithmetic >> >> So, let me re-phrase my statement... in any realistically complex >> arithmetic that is consistent with operations performed for real-world >> applications (e.g. multiplication, division, exponentiation, ...), one >> cannot demonstrate a bullet-proof proof of 1+1=2. Better? :) > > Well, Peano arithmetic is normal, everyday arithmetic fully axiomatized, > and Presburger arithmetic is a subset of it, so we can utilize the fact > that 1 + 1 = 2 is provable in Presburger arithmetic (damn is my spell > checker getting a workout on this sentence) to prove it in Peano > arithmetic, and therefore in everyday use. Alas, that's not the case. Peano arithmetic is undecidable: http://mathworld.wolfram.com/PeanoArithmetic.html Oh, and this may be of interest: http://scienceblogs.com/goodmath/2006/06/extreme_math_1_1_2.php -- Steven -- http://mail.python.org/mailman/listinfo/python-list
