Given two functions and from to , the notation
means that the ratio stays bounded as . If moreover that ratio approaches zero, we write
It is legitimate to write, say, , with the understanding that we are using the equality sign in an unsymmetric (and informal) way, in that we do not have, for example, .
means that the ratio is bounded away from zero as , or equivalently .
If both and , we write .
One more notational convention in this group is
where denotes the logarithmic integral.
Landau notation is also handy in applied mathematics, e.g. in describing the time complexity of an algorithm. It is common to say that an algorithm requires steps, for example, without needing to specify exactly what is a step; for if , then for any positive constant .
|Date of creation||2013-03-22 11:42:56|
|Last modified on||2013-03-22 11:42:56|
|Last modified by||Mathprof (13753)|