Saturday 23 November 2013

Is it possible to divide the lines

Is it possible to divide the lines in the plane into pairs of perpendicular lines so that
every line belongs to exactly one pair?
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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, &a...