1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

If A,B denumerable prove AUB denumerable

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that if A and B are denumerable sets, not necessarily disjoint, then AUB is denumerable.


    2. Relevant equations



    3. The attempt at a solution
    So I started my saying that since A and B are denumerable then, f:N-->A and g:N-->B are bijections. The I defined h(n) in terms of f and g as such:
    h(n) = f(n/2) if n is even
    h(n) = g((n+1)/2) if n is odd
    This is all I have so far. I am not sure where to go or what this tells me.
     
  2. jcsd
  3. Apr 2, 2009 #2
    Try mapping the sets to the naturals, the maps have to be injective. A hint is that n->2n is an injection and composition of injective functions is injective.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: If A,B denumerable prove AUB denumerable
  1. Denumerable sets (Replies: 9)

  2. A denumerable question (Replies: 4)

Loading...