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Is there a difference between these two limits? $$\lim_{x\rightarrow\infty}f(x)=+\infty\text{ and }\lim_{x\rightarrow+\infty}f(x)=\infty$$

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    $\begingroup$ $\infty$ generally denotes $+\infty$ much like $1$ and $+1$. $\endgroup$ – Jika May 8 '14 at 19:20
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    $\begingroup$ On the Riemann sphere, for instance, there is only one point at infinity. $\endgroup$ – Lucian May 8 '14 at 19:28
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There is absolutely no difference, it is just that sometimes it is good to be explicit, seeing sometimes you may have "$-\infty$" so the people use "$+\infty$" to make things very clear.

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No.

$+\infty$ and $\infty$ are syntactically equivalent and can be used interchangeably.

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