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A function of real numbers is also called a step function if it is piecewise constant function involving a finite number of inputs. There are two types of step functions. Greatest Integer function (floor function) - A function f(x) is said to be a floor function which possesses biggest integer that is less than or equal to the input value x Smallest Integer function (ceiling function) - A function f(x) is said to be a ceiling function which is composed of the lowest integer that is either bigger or equal to the input value x A step function is also known as staircase function, since it looks like a staircase.
The prime counting function Ï(n) is defined as the number of primes not greater than n. For example, Ï(11) = 5, since there are five primes less than or equal to 11. There are known algorithms to compute exact values of Ï(n) faster than it would be possible to compute each prime up to n.