Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sets and classes

  1. Aug 18, 2008 #1
    The stupid question of the day:

    The existence of proper classes is often proven by contradiction: assume that some object is a set, you'll find a contradiction, therefore it is not a set. We baptized those as "classes".

    Will (can) this even happen to classes? To find some object, assume it is a class, and get a contradiction, proving it is something else?
     
  2. jcsd
  3. Aug 18, 2008 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Except for the question of internal vs external in nonstandard analysis, I can't think of any situation in ordinary mathematics where such a thing could come up. The only reason we see it with sets and classes is because one of the main applications of sets is to serve as a simplified yet extensive version of higher-order logic.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook