Friday, 11 October 2013

Difference of Numbers

Divide the numbers 1, 2, 3, 4, 5 into two arbitrarily chosen sets. Prove that one of the sets contains two numbers and their difference.
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Define f:R→R by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...