Let be an integer variable which tends to infinity and let be a continuous variable tending to some limit. Also, let or be a positive function and or any function. Then Hardy and Wright (1979) define
1. to mean that for some constant and all values of and ,
2. to mean that ,
3. to mean that ,
4. to mean the same as ,
5. to mean , and
6. to mean for some positive constants and .
implies and is stronger than .
The term Landau symbols is sometimes used to refer the big-O notation and little-O notation . In general, and are read as "is of order ."
If , then and are said to be of the same order of magnitude (Hardy and Wright 1979, p. 7).
If , or equivalently or , then and are said to be asymptotically equivalent (Hardy and Wright 1979, p. 8).
See alsoAlmost All,
Asymptotic,
Big-O Notation,
Big-Omega Notation,
Big-Theta Notation,
Landau Symbols,
Little-O Notation,
Order of Magnitude,
Tilde Explore with Wolfram|Alpha ReferencesHardy, G. H. and Wright, E. M. "Some Notations." §1.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 7-8, 1979.Jeffreys, H. and Jeffreys, B. S. "Increasing and Decreasing Functions." §1.065 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, p. 22, 1988. Referenced on Wolfram|AlphaAsymptotic Notation Cite this as:Weisstein, Eric W. "Asymptotic Notation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AsymptoticNotation.html
Subject classificationsRetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4