\begin{definition}[Definition:Set/Implicit Set Definition/Infinite Set]
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.'''
\end{definition}