Definition:Enumeration

Notation
In order to avoid tedious case distinctions between finite and countably infinite sets, many authors write:


 * Let $X = \left\{{x_1, x_2, \ldots}\right\}$ [...]

implying that $X$ be countable, but not excluding the possibility that $X$ is actually finite.

Some authors use the abbreviated notation $\left\{{x_1}\right\}$ for both.

Also see

 * Definition:Sequence, of which enumerations are specific examples
 * Definition:Countable