# 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.