Real Analysis

$I(n)\sim 1$ (roughly constant)

$I(n)\to\infty$ but $I(n) = o(n)$ (sub-linear)

$I(n)\sim n$ (roughly linear)

$I(n)/n\to\infty$ but $I(n)$ is finite for all $n$

$I(n) = \infty$ for all sufficiently large $n$