If all the elements in set A can be found in set B, and the number of elements in set A is less than that in set B, then set A is called the proper subset of set B.

Example: Set A {1, 2,3} Set B {1, 2,3,4} proper subset, where A is B. If set b {1, 2,3} cannot be proper subset, then it can only be a subset. Generally speaking, some (but not all) elements in set B can be taken out to form a new set A, so this new set A is the proper subset of set B..

Special case: An empty set is the proper subset of any non-empty set.