relating to or of the nature of an asymptote; "an asymptotic function"

Concerning the rate at which a function grows, ignoring constant factors. For example, if an algorithm uses 3n+5 steps on inputs of size n, we say its running time is "asymptotically linear" - emphasizing that the linear dependence on n is what's important, not the 3 or the 5.

Approaching indefinitely near, yet never meeting.