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In French, we say that $f$ est équivalente à $g$ denoted by $f \sim g$ for a limit point $x_0$ of a topology when $$\lim\limits_{x \to x_0} \frac{f(x)}{g(x)} = 1.$$

This is the first level of asymptotic expansion in English. However it seems that the word equivalent cannot be used in English.

Is there an appropriate wording in English for "first level of asymptotic expansion"?

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    $\begingroup$ You would just say $f$ is asymptotic to $g$ $\endgroup$ – πr8 Jan 10 '16 at 10:29
  • $\begingroup$ You can say $f$ is asymptotically equivalent to $g.$ $\endgroup$ – daniel Jan 10 '16 at 11:11

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