1,792
edits
Changes
Jump to navigation
Jump to search
Line 192:
Line 192: + +
→Unique square root of -1 necessary for complex analysis: A proof is either rigorous or it is not
:::::::: Responding to Frederick, I would never doubt that complex numbers can be useful. So are approximations, estimates, predictions about the future, intuition, and prayer. The issue is whether a mathematical proof that resorts to use of complex numbers is as rigorous as an [[elementary proof]]. The answer is obviously "no".--[[User:Aschlafly|Andy Schlafly]] 01:17, 10 April 2012 (EDT)
:::::::: Responding to Frederick, I would never doubt that complex numbers can be useful. So are approximations, estimates, predictions about the future, intuition, and prayer. The issue is whether a mathematical proof that resorts to use of complex numbers is as rigorous as an [[elementary proof]]. The answer is obviously "no".--[[User:Aschlafly|Andy Schlafly]] 01:17, 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)
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)