1. Referring to an asymptote or not falling together.
2. Approaching a given value as an expression containing a variable tends to infinity.
3. Of two functions, so defined that their ratio approaches unity as the independent variable approaches a limit or infinity.
4. With reference to a formula, becoming increasingly exact as a variable approaches a limit, usually infinity.
5. Coming into consideration as a variable approaches a limit, usually infinity: asymptotic property; asymptotic behavior.