different between asymptotic vs asymptote

English

Etymology

From asymptote +? -ic.

Pronunciation

• (UK) IPA^(key): /?æs?m(p)?t?t?k/
• (UK) IPA^(key): /?æs?m(p)?t?t?k/
• Rhymes: -?t?k

Adjective

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 and 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

Synonyms

• asymptotical

Derived terms

• asymptotic analysis
• asymptotic curve
• asymptotic stability

Translations

English

Etymology

circa 1650, from Ancient Greek ????????? (asúmpt?t?), the feminine of Apollonius Pergaeus' (circa 200 BC) Ancient Greek adjective ?????????? (asúmpt?tos, “not falling together”), from ? (a, “not”) +? ??? (sún, “together”) +? ?????? (pt?tós, “fallen”).

Pronunciation

• (General American) IPA^(key): /?æs?mpto??t/, /?æs?mto??t/, /?e??s?mto??t/, /?æs?mt?t/

Noun

asymptote (plural asymptotes)

1. (mathematical analysis) A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".
2. (by extension, figuratively) Anything which comes near to but never meets something else.
   • 1860: Frederic William Farrar, An Essay on the Origin of Language, page 117

     Language, in relation to thought, must ever be regarded as an asymptote.

Derived terms

Translations

Verb

asymptote (third-person singular simple present asymptotes, present participle asymptoting, simple past and past participle asymptoted)

1. (mathematical analysis) To approach, but never quite touch, a straight line, as something goes to infinity.
   • 2006: Neil deGrasse Tyson, The Perimeter of Ignorance

     As you become more scientific, yes, the religiosity drops off, but it asymptotes.

References

French

Etymology

Borrowed from Ancient Greek ?????????? (asúmpt?tos).

Pronunciation

• IPA^(key): /a.s??p.t?t/

Noun

asymptote f (plural asymptotes)

1. (mathematical analysis) asymptote

Derived terms

• asymptotique

Further reading

• “asymptote” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).