ASL STEM

Definition

A proper subset S' of a set S is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is therefore a proper subset of any nonempty set.

Source: http://mathworld.wolfram.com/ProperSubset.html

Example

For example, consider a set {1,2,3,4,5}. Then {1,2,4} and {1} are proper subsets, while {1,2,6} and {1,2,3,4,5} are not.