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Talk:Elementary proof (view source)

Revision as of 15:19, April 10, 2012

474 bytes added ,  15:19, April 10, 2012
→‎Unique square root of -1 necessary for complex analysis: a proof that relies on the Axiom of Choice is not as good as one that solves the same problem without resorting to that axiom.
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::::::::: Obvious? On the contrary, no mathematical proof is more rigorous than any other mathematical proof. A proof is either rigorous or it is not, whether it uses complex numbers or any other mathematical construct. [[User:RSchlafly|RSchlafly]] 01:52, 10 April 2012 (EDT)
 
::::::::: Obvious? On the contrary, no mathematical proof is more rigorous than any other mathematical proof. A proof is either rigorous or it is not, whether it uses complex numbers or any other mathematical construct. [[User:RSchlafly|RSchlafly]] 01:52, 10 April 2012 (EDT)
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:::::::::: That's unnecessary semantics.  Replace "rigorous" with whatever substitute you prefer, but a proof that relies on fewer or less doubtful assumptions is more [rigorous/robust/credible/advantageous] than one that relies on many or more doubtful assumptions.  For example, a proof that relies on the [[Axiom of Choice]] is not as good as one that solves the same problem without resorting to that axiom.--[[User:Aschlafly|Andy Schlafly]] 11:19, 10 April 2012 (EDT)
    
Slightly off-topic, but you might be interested in physical evidence for complex numbers. According to this new paper [http://arxiv.org/abs/1204.1858], imaginary numbers are the most crucial difference between classical and quantum mechanics. [[User:RSchlafly|RSchlafly]] 20:50, 9 April 2012 (EDT)
 
Slightly off-topic, but you might be interested in physical evidence for complex numbers. According to this new paper [http://arxiv.org/abs/1204.1858], imaginary numbers are the most crucial difference between classical and quantum mechanics. [[User:RSchlafly|RSchlafly]] 20:50, 9 April 2012 (EDT)
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