Axiom of Choice


The Axiom of Choice states that for any set A of sets, there exists a choice function which picks a single element of each x in A. While intuitive, it has some surprising consequences, such as the Banach-Tarski Paradox. It is logically independent of the Zermelo-Frankl axioms, so one may choose whether or not to include it.


This concept has the prerequisites:


  • Know the statement of the Axiom of Choice
  • Be aware that it is controversial (e.g. because of the Banach-Tarski paradox), and it is often noted specifically when a theorem depends on it
  • Be aware that it is independent of the Zermelo-Frankl axioms

Core resources (read/watch one of the following)



See also

-No Additional Notes-