1. The problem statement, all variables and given/known data Assume that (xn) and (yn) are sequences, both of which converge to L. Assume further that (zn) is a sequence satisfying xn <or= zn <or= yn for all n in N. Prove that (zn) also converges to L 2. Relevant equations 3. The attempt at a solution Let xn and yn be sequences that converge to L and let zn converge to L' The fact that xn is <or= to zn for all n in N implies that L<or=L' The fact that zn is <or= to yn for all n in N implies that L'<or=L' Meaning L<or=L'<or=L Therefore, L=L' Would this be correct? Do I need to show that Zn converges before I assume it has a limit?