In mathematics, the useful concept of a process with no end.
As represented by the symbol ∞, it is often mistakenly thought to be the largest number or a place on the real number line. Instead, it is the idea of a limit, as in the expression x → ∞, which suggests that the variable x increases without bound. For example, the function f (x) = 1/ x , or the reciprocal of x , tends toward 0 as x approaches infinity as a limit. This process of approaching is crucial to the definition of the derivative and the integral in calculus, as well as to many other concepts of mathematical analysis .