A review of discrete probability and sets


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  • The following topics will be covered in this lecture:
    • A review of basic set theory
    • A review of basic probability theory
    • Some basic probabilistic experiments with finite sample spaces
    • Sampling procedures

Basic set theory: a history of sets

  • In the nineteenth century, the German mathematician Georg Cantor developed the greater part of today’s set theory.
  • Set theory is at the basis of mathematical logic and how, similar to computing, mathematical objects are ordered in hierarchies of classes with certain properties.
  • At the turn of the nineteenth and twentieth centuries, Ernst Zermelo, Bertrand Russell, Cesare Burali-Forti and others found contradictions in the originally proposed set theory, with one of the famous results being Russell’s paradox.