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
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