Below is the formal definition of limxa f(x) = L.

(I have omitted the domains to make it clearer. The domains of variables and are the set of positive real numbers (R +), the domain of x is the set of real numbers (R))

Express limxa f(x) not equals L by finding the negation of the formula and simplifying .

x,(0 < |x a| < |f(x) L| < )