Definition:Enumeration/Also defined as

Enumeration: Also defined as
Some sources define an enumeration as starting from $0$ rather than $1$.

Hence for a finite enumeration, one would write:
 * Let $X = \set {x_0, x_1, \ldots, x_{n - 1} }$

and for an infinite enumeration:
 * Let $X = \set {x_0, x_1, x_2, \ldots}$

It is unimportant which convention is used.