Continuous function
Karl Weierstraß gave another definition of continuity: Imagine a function f, defined on the real numbers. At the point  the function will have the value . If the function is continuous at , then for every value of  no matter how small it is, there is a value of , so that , means that . We can put this another way, given a point close to  (called x), the absolute value of the difference between the two values of the function can be made increasingly small, if the point x is close enough to .