Problem 1: If \(L\) is the greatest lower bound of the sequence \(a_n\), find the set of lower bounds of \(a_n\).
Problem 2: Prove or disprove that \(\lim\limits_{n \to \infty}a_n = a\) and \(\lim\limits_{n \to \infty}a_n = a' \implies a = a'.\)
Problem 3: If \(M\) is the least upper bound of \(a_n\), and \(a_n\) is non-decreasing, then prove that \(\lim\limits_{n \to \infty}a_n = M\).