A Crash Course in Set Notation

Set notation is the language of modern mathematics and computer science. It provides a way to define and formalize many notions such as algebraic and data structure. It provides formality and brevity much needed mathematics and computer science.

What is a set?

A set is a collection of unique objects. These objects are placed within curly braces “\{ \}“. For example a set of animals can be \{ cat, dog, snake \} or \{ bird, cow, fish \}. This way of writing a set is called the tabular form, a more common way is defined as follows:

\{ x | x satisfies some properties \}

The vertical line stands for “such that”. The set of farm animals or animals that lives on a farm is written as \{x | x is an animal that lives on a farm \}.


  1. What is a set?
  2. Basic Notations
  3. Union and Intersection
  4. Number Sets
  5. Complement, Power set and Cartesian Product
  6. Functions
  7. Applications

Filed under Crash Courses, Computer Science, Mathematics

Sources Used

  • Naive Set Theory by Paul R. Halmos
  • Schaum’s outline of Set Theory by Seymour Lipschutz
  • Chapter Zero by Carol Schumacher
  • Fundamental Concepts of Computer Science by Leon S. Levy

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