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Mathematics LibreTexts

1: Sets

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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 × to get a new set A×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.
  • 1.8: Sets That Are Number Systems
  • 1.9: Russell’s Paradox


This page titled 1: Sets is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by Richard Hammack.

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