1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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


    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