A function f (x ) has limit L as x tends to c if given any positive number ∊ (no matter how small) there is a positive number δ such that if x is in the domain of f, x is not c, and x - c δ, then f (x ) - L < ∊; written

A sequence {a_n:n = 1, 2,...} has limit L if given a positive number ∊ (no matter how small), there is a positive integer N such that for all integers n greater than N, a_n - L ∊.