Elementary questions about functions, notation, properties, and operations such as function composition.

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$f(nx)\to 0$ as $n\to+\infty$

Let $f:\mathbb R^+\to\mathbb R^+$ be a continuous function that has the following property: For any $x\in I$, $f(nx)\to 0$ as $n\to+\infty$. Intuitively, if $I$ is 'big' enough, $f$ necessarily ...