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    http://books.google.co.uk/books?id=I...esult&resnum=8

    I can't understand this proof.

    I understand the f(i)<k+1 bit. But then I'm not really that convinced about explanation thats its injection. It just seems to say the obvious that if m\leq k \Rightarrow m\leq k+1 but still yeah I understand how the restricted function is injection by the inductive hypothesis. So that bits alright.

    But its f(i)=k+1 for some i in N_m that is giving me trouble. I don't understand what the function g is doing.

    Anyone?

    Its page 133 or chapter 11 if it doesn't go to the section.

    P.S. The lemma is so obvious too.
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    G is pimping out dem hos.

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    I don't know about anyone else, but google books is telling me that pages 125-153 aren't part of the preview, so we can't see the proof.
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    Click on 11 Properties of a finite sets

    Its the first lemma proof. Not the actual Pigeonhole principle. I just don't understand the lemma that is used in the proof of the contraposition of Pigeonhole principle.

    This lemma
    If there exists an injection N_m \rightarrow N_n then m \leq n
 
 
 
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