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Homework Help: 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.
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