What indicates that a point on a number line is not included in the set?

The presence of an open circle on a number line serves as a visual representation indicating that a specific point is not included in the set. This notation is crucial when depicting intervals, particularly in cases involving inequalities. For instance, if the interval is expressed as ( x < 5 ), an open circle is placed on the number 5 to show that while all values less than 5 are included, the value of 5 itself is not.

The usage of an open circle informs anyone interpreting the graph that the endpoint does not belong to the solution or the set of numbers being represented. This is particularly important in mathematical contexts where differentiating between inclusive (closed circle) or exclusive (open circle) boundaries can change the understanding or outcome of an inequality or set scenario.