asymptotic

From asymptote +‎ -ic.

• (UK) IPA^(key): /ˌæsɪm(p)ˈtɒtɪk/
• (US) IPA^(key): /ˌæsəm(p)ˈtɑtɪk/, /ˌæsəm(p)ˈtɔtɪk/
• Rhymes: -ɒtɪk

asymptotic (not comparable)

1. (mathematics) Pertaining to values or properties approached at infinity.
   • 2011, Soon-Mo Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, →ISBN, page 130:

     F. Skof investigated an interesting asymptotic property of the additive functions (see Theorem 2.34). In fact, she proved that a function f : E₁ → E₂ is additive if and only if ‖f(x + y) − f(x) − f(y)‖ → 0 as ‖x‖ + ‖y‖ → ∞, where E₁ is a normed space and E₂ is a Banach space.

   • 2011, Vera Koponen, "Some connections between finite, infinite model theory", Finite and Algorithmic Model Theory, Cambridge University Press, →ISBN, page 110:

     More recently, a direction of research initiated by Macpherson and Steinhorn [28] and continued by Elwes [13, 14] and Ryten studies classes of finite structures in which definable sets have a uniform asymptotic behaviour, as the cardinalities of the universes increase.

2. (mathematical analysis) Coming into consideration as a variable tends to a limit, usually infinity.

   The asymptotic behavior of a function

• asymptotical