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May 27th, 2008, 05:35 AM   #1
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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.
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May 27th, 2008, 06:05 AM   #2
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Re: Cardinality Proof Question, Please help.

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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