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QED
QED: Beauty in Mathematical Proof by Burkard Polster is a short book with some elegant proofs (about 1 per page) from elementary geometry and number theory. Here are two that caught my eye. I know that .999.... =1 but I have always thought of this as something like a convention. Not so. Here is the proof.
Let x=.999...
then 10x=9.999...
now subtract x from both sides and we get
9x=9 or x=1
QED
And here is a just too lovely proof for the sum of the first n natural numbers.
Posted by Alex Tabarrok on August 23, 2004 at 07:40 AM in Science | Permalink
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» 0.999... = 1? from Mahalanobis
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