asymptotically

[ as-im-tot-ik-lee ]

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.

Word History and Origins

Origin of asymptotically¹

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

Example Sentences

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

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

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

From Literature

And there are electronic keyboards, more and more sophisticated, asymptotically approaching the sound of an acoustic piano.

From New York Times

For a particular well, the engineer might estimate that each year’s production would be 15 percent less than the previous year’s production, over the life of the well, asymptotically approaching zero.

From Forbes