Singleton set in the context of Event (probability)

Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events (see § Events in probability spaces, below).

In Euclidean geometry, the intersection of a line and a line can be the empty set, a single point, or a line (if they coincide). Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.

In a Euclidean space, if two lines are not coplanar, they have no point of intersection and are called skew lines. If they are coplanar, however, there are three possibilities: if they coincide (are the same line), they have all of their infinitely many points in common; if they are distinct but have the same direction, they are said to be parallel and have no points in common; otherwise, they have a single point of intersection, denoted as singleton set, for instance ${\displaystyle \{A\}}$.