Big-O, big-Theta, And big-Omega notation can be extended to functions in more than one variable. For example, the statement is means that the exist constants C, k1 , and k2 such that whenever and .
Show that is O(xy).
In this problem we need to show that
Let us consider f and g are functions from the set of integers to the set of real numbers.
The estimate value can be said that f(x) is O(g(x)) if there are constants C and k such that
, where C > 0 and x> k.The constants C and k are called the witnesses to the relationship.
The definition of f(x) is O(g(x)) says that f(x) grows slower than some fixed multiple of g(x) as x grows without bound.