1. The problem statement, all variables and given/known data Let A be a finite subset of R. For each n in N, let x_n be in A. Show that if the sequence x_n is convergent then it must become a constant sequence after a while. 2. Relevant equations The definition of limit. 3. The attempt at a solution As A is finite, at least one element of A will appear in the sequence more than once after some N. As this sequence is convergent there is an M for any ε such that |x_n - x| < ε for every n with n>M. Let M>N.... Help please. I can't decide whether this problem is too hard or I'm stupid or this is just because I'm a beginner?