Let S be a set of intervals, or segments.

Let S be the set of all natural numbers for which P(n) is false.

Let S be a set with v elements.

Let S be a set of n 2-dimensional points.

Let S be the surface boundary of the volume V.

Let S be a vector space over the real numbers, or, more generally, some ordered field.

Let S be a set of q elements and d a positive integer.

Let S be a semigroup with zero element 0.

Let S be a set of 2n elements.

For instance, on the unit circle, let S be the set of points for which is a rational number.