[for all of the following, "lim" means the limit as n->∞] Let an be a sequence of real numbers. Theorem: if lim an = L and lim an = M, then L=M. (Incorrect) "Proof": lim an = L and lim an = M Thus, L = lim an = lim an = M (transitive property) Therefore, L=M. To me, every step in the proof seems to be justified and correct. Can someone please explain what is wrong with this proof?