Results 1 to 4 of 4

Math Help - Closed Under Addition

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    37

    Closed Under Addition

    Find a subset of Z that is closed under addition but is not a group of the additive group Z.

    Will the set of natural number be suffice?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by MissMousey View Post
    Find a subset of Z that is closed under addition but is not a group of the additive group Z.

    Will the set of natural number be suffice?
    Well, that depends how you define the naturals. Why do you think that will work?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    Posts
    37
    Quote Originally Posted by Drexel28 View Post
    Well, that depends how you define the naturals. Why do you think that will work?
    Let S be the set of even natural numbers where S = {2, 4, 6, ...}. This will be closed with respect to addition because the sum of two even natural numbers is an even natural number.

    However, since the set does not contain inverses and does not contain the identity element, it does not satisfy group properties.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,541
    Thanks
    1394
    There are two commonly used definitions of the "natural numbers"- all positive integers or all non-negative integers. Either of those will work for this problem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is R-P closed under addition?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 5th 2011, 09:37 PM
  2. Finite set of integers closed under addition
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 4th 2010, 04:24 AM
  3. Metric Space, closed sets in a closed ball
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 19th 2009, 05:30 PM
  4. Closed Linear Operators/Closed Graph Theorem
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: June 17th 2009, 02:36 AM
  5. Closed Under Addition Proofs
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: November 4th 2008, 06:31 AM

Search Tags


/mathhelpforum @mathhelpforum