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anticorncob28


Joined: Thu May 05, 2016 10:31 pm Posts: 41 Location: Nebraska, USA

According to GĂ¶del's first imcompleteness theorem, any selfconsistent system has a statement that is independent of the system. I don't understand how this is true. Take the real numbers. There are several constructions of the real numbers, and they all demonstrably describe a unique system up to isomorphism. How then can there exist a statement P about the real numbers which can be neither proven nor disproven? Then you can invent two real number systems, one in which P is true and one in which P is false. But that can't be the case if the two real number constructions are isomorphic.
_________________ "Climate change is the canvas on which the history of the 21st century will be painted." Mark Lynas, Six Degrees: Our Future on a Hotter Planet





GiantEvil


Original Member
Joined: Sat Aug 06, 2011 10:19 am Posts: 786

_________________ It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence. W. K. Clifford






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