Assume $a_n$ is a monotonic increasing sequence that tends to $\infty$, and assume that $(a_{n+1}/a_n)$ tends to 1. Now, let $f:R\to R$ be a continuous function such that for all $x>0$ we have $f(a_nx)$ tends to $0$ as $n$ increases. Is it necessarily true that $f(x)$ tends to $0$ at $\infty$?
Perhaps a simple question about a continuous function
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real-analysis
general-topology
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0Just a tip, to type $a_{n+1}$, type "a_{n+1}" – 2017-02-05
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0Thank you! couldn't get that to work. – 2017-02-05
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0I see that this question has already been asked, see http://math.stackexchange.com/questions/2116656/forall-x0-lim-n-to-inftyfa-nx-0-then-lim-x-to-inftyfx-0. – 2017-02-05