- What is the number less than one closest in value to one?
- I haven't actually read the proof, but I'm not convinced by it. 0.999... is definitely smaller than 1, or it would be called 1.
I believe it is just common sense.
Illiteracy might no longer be a problem in the developed world, but innumeracy is rampant. :-)
4 comments:
Well, at least according to Paul Graham, American high schools are little more than prisons, with actual learning located somewhere far down on the list of priorities of both students and teachers...
I think the Wikipedia article has a good section on why many people find it hard to accept, or make such mistakes. I don't think it is uniquely American. Part of it is probably bad pedogogical techniques of teaching limits, but some of it is probably the difficulty of dealing with notions they often don't encounter in everyday usage of notation and counting.
There are similar examples in physics. Many people will refuse to accept results in Quantum Mechanics that defy common cense notions, and it is even a troubling problem for those who understand QM 100%.
Indirect nature of some proofs can also confound some people. There are still people who refuse to accept the impossibility of squading the circle or trisecting the angle, and Marilyn Vos Savant, undoubtly a smart lady, albeit not academically trained in advanced Mathematics, refused to accept Wiles's proof of Fermats Last Theorem just because it used elliptic curves.
My sympathies go to the people who are requested to submit an intelligent answer to this sort of question on a test.
Any evidence of creativity will be punished!
Creativity in math stems from giving elegant and correct proofs.
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