1.1. Notation and Set Theory
Definition 1.1.1: Sets and Operations on Sets
A set is a collection of objects chosen from some universe. The universe is usually understood from the context. Sets are denoted by capital letters or curly brackets.
- A B: A is a subset of B means that every element in A is also contained in B.
- A B: A union B is the set of all elements that are either in A or in B or in both sets.
- A B: A intersection B is the set of all elements that are in both sets A and B.
- A \ B: A minus B are all elements from A that are not in B.
- comp(A): The complement of A consists of all elements that are not in A.
- Two sets are disjoint if A B = 0 (the empty set)
- Two sets A and B are equal if A B and B A