Recent content by app_oos

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    Proof by induction: nCr always an integer

    This is the only part I don't get. I know nCr was assumed to be an integer (induction hypothesis) but where was nC(r-1) assumed to be an integer? Is this some sort of axiom, that if nCr is an integer, then nC(r-1) is one too? I understand the other parts of the proof and I know what induction...
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    Proof by induction: nCr always an integer

    But you're trying to prove that any nCr will be an integer by induction. If you haven't proven it yet, then how can you say that nC(r-1) will be an integer?
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    Proof by induction: nCr always an integer

    Ok, so he says that {n+1}Cr = nCr + nC{r-1}, which I understand. What I don't get is how it "follows" that {n+1}Cr is an integer as well, since you would need to show that both nCr and nC{r-1} are integers to use the closure property. We know the first one by assumption, but how do you know...
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    Proof by induction: nCr always an integer

    What I'm asking is, how do you show nC(r-1) is an integer?
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    Proof by induction: nCr always an integer

    I understand that {n+1}Cr = nCr + nC{r-1}, but can someone tell me why it follows that {n+1}Cr are natural numbers just from that statement and the inductive hypothesis that nCr is all natural numbers?
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