asymptotically
|a-symp-tot-ic-al-ly|
🇺🇸
/ˌeɪsɪmˈtɑːtɪkli/
🇬🇧
/ˌeɪsɪmˈtɒtɪkli/
(asymptotic)
approaching without meeting
Etymology
'asymptotic' originates from New Latin 'asymptoticus' and French 'asymptotique', ultimately from Greek 'asymptōtos', where 'a-' meant 'not' and 'symptōtos' meant 'falling together (meeting)'.
'asymptotic' changed from Greek 'asymptōtos' into Late Latin/Medieval scientific Latin and French forms such as 'asymptota'/'asymptotique', and eventually entered modern English scientific usage as 'asymptotic' (with the adverb 'asymptotically').
Initially it meant 'not falling together' (describing lines or curves that do not meet), but over time it evolved to the modern mathematical sense of 'approaching a limit without necessarily reaching it'.
Meanings by Part of Speech
Adverb 1
in a manner that approaches a particular value, condition, or behavior arbitrarily closely as some parameter (often a variable) tends to a limit (frequently infinity).
As n grows large, f(n) is asymptotically equal to n^2.
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Adverb 2
used in analysis of algorithms or functions to describe growth rates or behavior up to factors that become negligible in the limiting case (e.g., asymptotically linear, asymptotically bounded).
The algorithm is asymptotically optimal, meaning no other algorithm has a strictly better growth rate for large inputs.
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Last updated: 2025/10/29 07:34