Let f be a function defined on some open interval that contains the number a, except possibly at a itself. We say the limit of f(x) as x approaches a is L, and we write

lim_(x → ∞) ( f(x) ) = L

if for every number ε > 0 there is a corresponding number δ > 0 such that

|f(x) - L| < ε whenever

0 < |x - a| < δ.