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Show that no injection exists for those infinite sets

  1. Nov 5, 2007 #1
    Let A,B,C be infinite sets. Suppose there is no injection from A to B and no injection from B to C. Prove there is no injection from A to C (without using cardinality and Schroeder-Bernstein).

    My current solution:
    Let f:A-> C. Assume f= s.r (. means composition), where r:A-> B and s:B-> C. If f is injective, then so is r (already proven), a contradiction. But what if we can't assume f= s.r?
     
    Last edited: Nov 5, 2007
  2. jcsd
  3. Nov 5, 2007 #2
    So f=s.r must be true?
     
  4. Nov 6, 2007 #3
    So, I'll stick with my current proof.
     
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