in english this reads as followsthe class of functions designated by og( )consists of all functions fwhere there exists greater than and an ( positive integersuch that is less than or equal to (nis less than or equal to times (nfor all greater than or equal to if is an element of og( ))we say that (nis og( )the function is called an asymptotic upper bound for in this case you may not be comfortable with the mathematical description above stated in english the set named og( )consists of the set of all functionsf( )that have an upper bound of dg( )as approaches infinity this is the meaning of the word asymptotic the idea of an asymptotic bound means that for some small values of the value of (nmight be bigger than the value of dg( )but once gets big enough ( bigger than )then for all bigger it will always be true that (nis less than dg(nthis idea of an asymptotic upper bound is pictured in fig for some smaller values the function' performanceshown in greenmay be worse than the blue upper bound linebut eventually the upper bound is bigger for all larger values of we have seen that the average time to access an element in list is constant and does not depend on the list size in the example in fig the list size is the in the definition and the average time to access an element in list of size is the (nfig an upper bound this copy belongs to 'acha