Appendix A: Sets and mappings
Shmuel Friedland, Mohsen Aliabadi · 2018
A set is any unordered collection of distinct objects. These objects are called the elements or members of the set. We indicate membership in or exclusion from a set using the symbols ∈ and ∉, respectively. The set containing no elements is known as the empty set. The set of elements common to two given sets A and B is known as their intersection and written as A ∩ B. The set of elements appearing in at least one of these sets is called the union, denoted by A ∪ B. We say that A and B are equal sets, written A = B, if these two sets contain precisely the same elements. Given sets A and B, whenever each element of A is also an element of B, we say that A is a subset of B and write A ⊆ B. If A and B have no elements in common, they are disjoint. Removing all elements from a set B that belong to another set A creates a new set: the set difference B ∖ A. We define the power set P (A) of a set A to be the set of all subsets of A, including the empty set and the set A itself.