formal definition of Landau notation
Let us consider a domain and an accumulation point . Important examples are and or and . Let be any function. We are going to define the spaces and which are families of real functions defined on and which depend on the point .
Suppose first that there exists a neighbourhood of such that restricted to is always different from zero. We say that as if
We say that as if there exists a neighbourhood of such that
In the case when in a neighbourhood of , we define as the set of all functions which are null in a neighbourhood of .
The families and are usually called ”small-o” and ”big-o” or, sometimes, ”small ordo”, ”big ordo”.
Title | formal definition of Landau notation |
Canonical name | FormalDefinitionOfLandauNotation |
Date of creation | 2013-03-22 15:15:48 |
Last modified on | 2013-03-22 15:15:48 |
Owner | paolini (1187) |
Last modified by | paolini (1187) |
Numerical id | 6 |
Author | paolini (1187) |
Entry type | Definition |
Classification | msc 26A12 |
Synonym | Landau notation |
Synonym | small o |
Synonym | big o |
Synonym | order of infinity |
Synonym | order of zero |
Related topic | PropertiesOfOAndO |