I know that there are different definitions for a limit point . "A number such that for all , there exists a member of the set different from such that . The topological definition of limit point of is that is a point such that every open set around it contains at least one point of different from ."-MATHWORLD Are they all equivalent, when defining "the limit of f"? Or, this may help too, does my definition of a limit sound correct?...(bold-faced variables are vectors) Let f: U->R^n Let a be an element of the reals such that for all delta' >0 there exists an x in U, different than a, such that ||x-a||<delta'. We say that lim f(x)=L as x->a, if for every epsilon>0 there exists a delta''>0 so that if ||x-a||<delta'' then ||f(x)-L||<epsilon. Also, Is it right that I used delta' and delta"?