find some c and n to show the function f is from big-o of function g.

For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that

f(n) < c * g(n), for each n>=n0

And this inherently means f(n) will never grow faster than g(n), for adequately large n->∞

Explanation:

The main purpose of the computational complexity is to categorize the algorithms about their show. And we can represent the T(n), which is the time function with the help of the big O notation, for showcasing an algorithm runtime complexity. As an example,

T(n) = O(n3)

proves that the algorithm has the cubic time complexity.

Now let's define Bio O, and from here we will get our answer. For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that

f(n) < c * g(n), for each n>=n0

And this inherently means f(n) will never grow faster than g(n), for adequately large n->∞

And this explanation gives us the value of c and N