Results 1 to 2 of 2

Thread: Sets containing unions, and vice versa

  1. #1
    May 2011

    Sets containing unions, and vice versa

    I've been going through some old exam papers, and I came upon an interesting part of a question that I'm not sure how to solve. Throughout the question I've been proving things like b\in b is false, at most one of b\in c and c\in b is true, and so on. I've been asked whether any of the following can occur, using only axioms (ZF1)-(ZF4) and (ZF9). (Extensionality, null set, pairs, unions, foundation.)

    1. x\in\bigcup x
    2. x\in\bigcup \bigcup x
    3. \bigcup x \in x

    I think (1) is false, by extension I think (2) is false (but can't get my reasoning right in my head), and I'm not sure about (3).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Feb 2010
    3. U{0} e {0}.

    Indeed, for any ordinal x, we have U(x+) = x and x e x+.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Aug 10th 2011, 05:45 PM
  2. How to I Find Angle (and Vice Versa)
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Nov 11th 2010, 12:30 PM
  3. Polar to Rectangular and Vice Versa
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Nov 8th 2009, 03:00 PM
  4. Replies: 3
    Last Post: Mar 30th 2009, 04:02 PM
  5. Replies: 1
    Last Post: Feb 12th 2006, 05:40 PM

Search Tags

/mathhelpforum @mathhelpforum