Sunday, 13 October 2013

an odd number of games

If 1 27 people play in a singles tennis tournament, prove that at the end of tournament,
the number of people who have played an odd number of games is even.

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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...