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Is there a mathematical symbol for "the value grows?"

For example:

This result will be increasingly difficult as the value of n grows to infinity.

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    What's wrong with $n \to \infty$? For that matter, what's wrong with "grows to infinity"?2012-10-02
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    Nothing wrong with the suggestion you proposed, I was just unaware of it's existance/usage.2012-10-02
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    If $(x_n)$ is a sequence, then $x_n\uparrow \infty$ means that $x_n$ tends to infinity increasingly, i.e. $x_n\leq x_{n+1}$ and $x_n\to\infty$. But there is really no need to write $n\uparrow \infty$ because $x_n=n$ is obviously increasing.2013-01-05
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    I've also seen $x_n\nearrow\infty$ for what Stefan writes as $x_n\uparrow\infty$. In general, $x_n\nearrow a$ or $x_n\uparrow a$ would mean that the sequence of the $x_n$ is increasing with limit $a$, and $x_n\searrow a$ or $x_n\downarrow a$ would mean that the sequence is decreasing and has limit $a$.2013-08-03
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    Be aware that $x_n\uparrow \infty$ is even the Knuth's up arrow notation for exponentiation i.e. $x_n^\infty$ (whatever this could mean in this situation)2015-09-01

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