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Mathematics LibreTexts

1: Sets

  • Page ID
    24799
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    • 1.1: Introduction to Sets
      A set is a collection of things. The things are called elements of the set. We are mainly concerned with sets whose elements are mathematical entities, such as numbers, points, functions, etc. A set is often expressed by listing its elements between commas, enclosed by braces. For example, the collection {2, 4, 6, 8} is a set which has four elements, the numbers 2, 4, 6 and 8. Some sets have infinitely many elements. For example, consider the collection of all integers.
    • 1.2: The Cartesian Product
    • 1.3: Subsets
    • 1.4: Power Sets
      Given a set, you can form a new set with the power set operation.
    • 1.5: Union, Intersection, Difference
      as numbers are combined with operations such as addition, subtraction and multiplication, there are various operations that can be applied to sets. The Cartesian product is one such operation; given sets \(A\) and \(B\), we can combine them with \(\times\) to get a new set \(A \times B\). Here are three new operations called union, intersection and difference.
    • 1.6: Complement
    • 1.7: Venn Diagrams
    • 1.8: Indexed Sets
      When a mathematical problem involves lots of sets, it is often convenient to keep track of them by using subscripts (also called indices). Thus instead of denoting three sets as A, B and C, we might instead write them as A1, A2 and A3. These are called indexed sets.
    • 1.9: Sets That Are Number Systems
    • 1.10: Russell’s Paradox