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|
|Date of creation||2013-03-22 15:15:48|
|Last modified on||2013-03-22 15:15:48|
|Last modified by||paolini (1187)|
|Synonym||order of infinity|
|Synonym||order of zero|