big notation the letter "oin big notation stands for orderin recognition that rates of growth are defined as the order of function we say that one function (nis big of another functionf( )and we define this as followsthe functiong( )of the input sizenis based on the observation that for all sufficiently large values of ng(nis bounded above by constant multiple of (nthe objective is to find the smallest rate of growth that is less than or equal to (nwe only care what happens at higher values of the variable represents the threshold below which the rate of growth is not importantthe function (nrepresents the tight upper bound (nin the following plot we see that (nn ( with and is approximately you will also see the notation (no( ( )this describes the fact that ( ( )is really set of functions that include all functions with the same or smaller rates of growth than (nfor exampleo( also includes the functions ( ) (nlogn)and so on