👉 In mathematics, a continuation is a type of limit that can be defined in a way that allows it to be approached from both sides. Continuities are important because they provide a way to define limits and show that certain functions converge or diverge. A function f(x) is continuous if for every x in the domain of f (a subset of the real numbers), the limit of f(x) as x approaches some other value y exists and is equal to f(y). This means that the