Results 1 to 2 of 2

Math Help - Set Theory

  1. #1
    Member
    Joined
    Dec 2006
    Posts
    79

    Set Theory

    Show that for all m,n in N, m<n if and only if m is a proper subset of n.

    Here is my reasoning.

    Assume m is a proper subset of n. Then m doesn't equal n by definition of a proper subset. Since m is a subset of n, then m must be less than n.

    Is this a concrete enough?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by taypez View Post
    Show that for all m,n in N, m<n if and only if m is a proper subset of n.

    Here is my reasoning.

    Assume m is a proper subset of n. Then m doesn't equal n by definition of a proper subset. Since m is a subset of n, then m must be less than n.

    Is this a concrete enough?
    The reasoning looks ok so far to me, but you have an "if and only if" which means you have to do the reverse. I'd probably try to say what you did a little fancier, like:

    Assume m is a proper subset of n. Then there is some x in n that is not in m (of course we'd use the symbols here, you noe the one that looks like a capital e and then the same symbol with a slash through it). Thus |m|<|n| for all m and n.

    Are you sure the question didn't ask |m|<|n|? That seems to be what you're proving.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 07:09 PM
  2. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 12:10 PM
  3. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 17th 2007, 10:52 AM
  4. Set theORY
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2007, 08:01 PM
  5. Set Theory
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 27th 2007, 10:22 AM

Search Tags


/mathhelpforum @mathhelpforum