asymptotically

American  

[as-im-tot-ik-lee] / ˌæs ɪmˈtɒt ɪk li /

adverb

1. Mathematics. in the way that the graph of a function approaches an asymptote, a straight line representing the limit of the function as one of its variables grows to infinity.

   This curve has a characteristic bell shape, high in the center but asymptotically approaching zero to form a tail on either side.

2. in an asymptotic way; in such a way as to approach a given value, point, level, etc., continuously without ever reaching it.

   He applies similar reasoning to the problem of the moral perfectibility of humankind, which he believes can only happen asymptotically over time.

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Etymology

Origin of asymptotically

First recorded in 1670–80; asymptotic ( def. ) + -ally ( def. )

Example Sentences

Ideas such as string theory, loop quantum gravity, canonical quantum gravity, and asymptotically safe gravity all attempt to bridge the gap.

From Science Daily • Mar. 9, 2026

One could even argue, taking Musk’s prediction to its logical conclusion, that the amount of physical effort needed to live day to day is asymptotically moving towards zero.

From Slate • Sep. 23, 2022

Boris Johnson said he wanted to renew his apologies, adding that the start of the pandemic was "an incredibly difficult time" and that it was not known that Covid could be transmitted asymptotically.

From BBC • Apr. 27, 2022

Fluid intelligence follows a developmental trajectory, reaching a peak in early adulthood and decreasing with age, whereas crystallized intelligence increases slowly and asymptotically as you age until fairly late in life.

From Salon • Nov. 4, 2018

On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies.

From "A Brief History of Time: And Other Essays" by Stephen Hawking