1. The problem statement, all variables and given/known data Let x_n be a convergent sequence with a ≤ x_n for every n, where a is any number. Prove that a ≤ lim x_n when n→∞. 2. Relevant equations Definition of limit. The usual ε, N stuff. 3. The attempt at a solution Let lim x_n = x and choose ε=x_n-a. Hence we have |x_n - x| < x_n - a which shows that -x<-a and thus x>a. Is this valid?