Results 1 to 2 of 2

Math Help - Choice functions for collections...

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    19

    Choice functions for collections...

    Find if possible a choice function for each of the following collections, without using the choice axiom:

    a. The collection A of nonempty subsets of Z+ (positive integers)
    b. The collection B of nonempty subsets of Z (integers)
    c. The collection C of nonempty subsets of the rational numbers Q
    d. The collection D of nonempty subsets of X^(omega), where X = {0, 1}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by iamthemanyes View Post
    Find if possible a choice function for each of the following collections, without using the choice axiom:

    a. The collection A of nonempty subsets of Z+ (positive integers)
    b. The collection B of nonempty subsets of Z (integers)
    c. The collection C of nonempty subsets of the rational numbers Q
    d. The collection D of nonempty subsets of X^(omega), where X = {0, 1}

    For (a) , for example , \forall\,X\in A\,,\,\,f(X):= the minimal element of X wrt the usual order

    on the natural numbers.

    You try now the other ones by yourself.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. union of collections
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: September 13th 2011, 05:37 PM
  2. [SOLVED] Choice functions
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 23rd 2011, 08:08 AM
  3. Collections of Bounded, Closed Subsets
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 8th 2010, 10:08 PM
  4. Infinite collections???
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 12th 2010, 09:45 AM
  5. Outer measure on collections of unions and intersections
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 4th 2009, 06:05 AM

Search Tags


/mathhelpforum @mathhelpforum