tudwell writes:
On a slightly related note, a friend and I were arguing over whether or not .999...=1. He contended that it didn't, while I contended that it did.
The funny thing is, as often as these forums (and similar forums) deal with unusual and unintuitive things from physics, I still think that deep down perhaps the Real Numbers are one of the most (the most!) unintuitive things humans ever created/discovered (take your pick).
One of my most well-worn pure mathematics books is Hermann Weyl's "Das Kontinuum" which deals with this fact.
For anybody here who knows this stuff and hasn't read it, he tries to construct the Reals using methods that would satisfy a finitist/intuitionist. In the end he constructs the Reals, but is unable to prove the fundamental theorem of calculus or the intermediate value theorem.
keresu writes:
don't forget, 1 = 0 too.
Although the proof contains a flaw. It's designed to test your knowledge of calculus. Same for the 2 = 0 "proof".
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