limit

Mathematical concept based on the idea of closeness, used mainly in studying the behaviour of functions close to values at which they are undefined. For example, the function 1/x is not defined at x = 0. For positive values of x, as x is chosen closer and closer to 0, the value of 1/x begins to grow rapidly, approaching infinity as a limit. This interplay of action and reaction as the independent variable moves closer to a given value is the essence of the idea of a limit. Limits provide the means of defining the derivative and integral of a function.