n.
In mathematics, a property of functions and their graphs .
A continuous function is one whose graph has no breaks, gaps, or jumps. It is defined using the concept of a limit . Specifically, a function is said to be continuous at a value x if the limit of the function exists there and is equal to the function's value at that point. When this condition holds true for all real number values of x in an interval, the result is a graph that can be drawn over that interval without lifting the pencil. Such functions are crucial to the theory of calculus , not just because they model most physical systems but because the theorems that lead to the derivative and the integral assume the continuity of the functions involved.