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

Is this true, if so is it obvious?

  1. Jun 12, 2008 #1
    There is no proper class such X such that every totally ordered set is isomorphic to a subclass of X.

    I'm using "proper class" and "isomorphic" rather liberally here, but you can assume them to be formulas in ZFC, or something.
     
  2. jcsd
  3. Jun 12, 2008 #2
    ? What about the class of all sets? Every set is a subclass of that, so certainly every totally ordered set is a subclass of it... Also, if you want something stricter; since the class of all sets is a class, you can consider the class of all totally ordered sets. Is your question whether or not that is a proper class? I'd think that it would be, but the way you asked your question, it sounds like the class of all sets should satisfy your requirement.

    Maybe I'm misunderstanding something here?
     
    Last edited: Jun 12, 2008
  4. Jun 12, 2008 #3
    No, you're right.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Is this true, if so is it obvious?
  1. True Probability (Replies: 5)

  2. Is this true? (Replies: 4)

  3. Is this true? (Replies: 6)

  4. True or false (Replies: 2)

Loading...