Definition:Set/Implicit Set Definition/Infinite Set

Definition
If the elements in a set have an obvious pattern to them, we can define the set implicitly by using an ellipsis ($\ldots$). If there is no end to the list of elements in the set, the ellipsis can be left open:
 * $S = \set {1, 2, 3, \ldots}$

which is taken to mean:
 * $S = $ the set containing $1, 2, 3, $ and so on for ever.

Also see

 * Definition:Infinite Set