Thursday 28 November 2013

f : R → R

Find all continuous functions f : R → R such that f(x) − f(y) is rational for
all reals x and y such that x − y is rational
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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...