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 May 27th, 2008, 06:35 AM #1 Newbie   Joined: Mar 2008 Posts: 11 Thanks: 0 Cardinality Proof Question, Please help. Hello, Can someone do this question please ? I can't do it. Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C| Note: |A| ≤ |B| means "there exist an injection from set A into set B" and so on for the rest. I would really appreciate it if someone can help me because I find this very hard.
May 27th, 2008, 07:05 AM   #2
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Quote:
 Originally Posted by Christi123 Hello, Can someone do this question please ? I can't do it. Prove that if |A| ≤ |B| and |B| ≤ |C| then |A| ≤ |C| Note: |A| ≤ |B| means "there exist an injection from set A into set B" and so on for the rest. I would really appreciate it if someone can help me because I find this very hard.
Let f: A --> B and g: B --> C be injections. Then define h: A --> C as h(x) = g(f(x)). h is an injection since g is an injection (and is defined since the range of f is in B).

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