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Introduction to Set Theory

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< Wikiversity < Wikiversity:School of Mathematics < School:Mathematics/Undergraduate/Pure Mathematics

Introduction to Set Theory


An introductory course from the School of Mathematics

This course aims to provide a thorough introduction to the subject of set theory. We will cover the following: Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences.

Course requirements

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The following knowledge is required or desirable on commencement of study of this course:

Course outline

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This is an approximate depiction of the course:

  • Propositional Logic
  • Axiomatic Approach
  • Unions and Intersections
  • Algebra of Sets
  • Ordered Pairs
  • Relations
  • Functions
  • Ordering Relations
  • Cardinal Arithmetic
  • Partial, Linear Orderings
  • Well Orderings
  • Comparison Theorem for Well Orderings
  • Isomorphisms
  • Transfinite Recursion Theorem
  • Replacement Axioms
  • Epsilon-Images
  • Ordinals
  • Ordinal Numbers
  • Ordinal Arithmetic

Lecture series

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Assignments

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Examinations

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Licensed under CC BY-SA 3.0 | Source: https://en.wikiversity.org/wiki/Introduction_to_Set_Theory
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