We can also use if it is a proper subset.

The smaller of the two classes is a proper subset of the larger class.

Other events are proper subsets of the sample space that contain multiple elements.

In particular, 2-perfect numbers are a proper subset of .

Unlike connected components, however, one module can be a proper subset of another.

Any set is a subset of itself, but not a proper subset.

A is then called a proper subset of B. Thus we write according to the emphasis required.

No proper (smaller) subset of the set fulfills the first property.

There is no proper subset of A having the first two properties.

The relation "is a proper subset of" is also not total.