Definition:Set/Implicit Set Definition/Infinite Set

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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