Hyperbolic 3-manifolds correspond to discrete subgroups of PSL(2,C). However, the limit of discrete subgroups may not remain discrete, and we may lose this correspondence. This poses challenges when attempting to extend certain properties to the limiting object of a sequence of manifolds. This talk will explore the conditions under which the limit of discrete subgroups of PSL(2,C) remains discrete, under two types of convergence: algebraic convergence and geometric convergence. Additionally, we will provide examples illustrating instances where the algebraic limit and geometric limit are distinct.