asymptotic
|a-symp-tot-ic|
🇺🇸
/ˌeɪsɪmˈtɑːtɪk/
🇬🇧
/ˌeɪsɪmˈtɒtɪk/
approaching without meeting
Etymology
'asymptotic' originates from Greek, specifically the word 'asymptōtos', where the prefix 'a-' meant 'not' and the root 'symptō' (from 'syn-' + 'piptein') meant 'to fall together'.
'asymptotic' changed from Greek 'asymptōtos' into Late Latin/Medieval Latin 'asymptoticus', passed into French as 'asymptotique', and eventually entered English as 'asymptotic' (modern scientific usage established in the 18th–19th centuries).
Initially it meant 'not falling together' (i.e., not meeting); over time it developed the technical mathematical sense 'approaching a line or limit without meeting it' and the related sense 'approaching a limiting value'.
Meanings by Part of Speech
Adjective 1
in mathematics: relating to an asymptote; describing a curve or function that approaches a line or value arbitrarily closely as the input grows (or tends to some limit) but does not meet it.
The function is asymptotic to the x-axis as x tends to infinity.
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Adjective 2
in statistics, physics, or general analysis: describing behavior or an approximation that becomes increasingly accurate or approaches a limiting value as some parameter (e.g., sample size, time, energy) grows.
Asymptotic results indicate the estimator's bias goes to zero as the sample size increases.
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Last updated: 2025/10/29 07:06