• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

set theory

  1. S

    Is the axiom of choice useful?

    This was brought up in another thread. Here is a post by W.D.Clinger. Wikipedia has a list of equivalent statements and theorems that follow from ZF+AC. I've heard of Tychonoff's theorem being important, but I've never really known why. The law of trichotomy for cardinal numbers and the...
  2. C

    John von Neumann and Recursively Defined Sets

    I've been reading Irreligion by John Allen Paulos, and I just came upon the following passage regarding John von Neumann's recursive definition of sets as an example of mathematical "creation" out of nothing: "The number 0 von Neumann simply defines to be the empty set. Then he takes the...

Back
Top Bottom