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My question is not about how to prove the following proof, as I already know how to do so. What I am more concerned about is the type of claim that is being made, and what am I really being asked to show; in particular when your claim is something relatively generalized, and you are brought to focus on a particular case that may occur within the general one. Below is the particular example of what I am talking about to be a bit more clear:

Let $x \in \mathbb{R}$ and $n \in \mathbb{Z}$ with $n > 0$. Show that $\lfloor\lfloor x \rfloor /n\rfloor = \lfloor x/n \rfloor$; in particular, $\lfloor\lfloor a/b \rfloor /c \rfloor = \lfloor a/bc \rfloor$ for all positive integers $a,b,c$.

I have shown both cases individually, but should I really only be proving the general case and acknowledging the particular case?

Note on tags: Even though the particular problem is that of elementary number theory, I do not believe my question should be tagged as such since my question is not particular to the subject of the question, but more so the form of the question.

Cameron Buie
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Alex
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    Often you just have to nod to the particular case (i.e. say "from the general case it is clear by choosing $x=a/b$ and $n=c$ that... ".) They are usually mentioned specifically because that particular instance is used a lot. – James Aug 09 '13 at 16:53

1 Answers1

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In instances like this, you should prove the general case, and then show how/why the particular case follows from it (often quite readily). It isn't wrong to prove the particular case separately, but it isn't ideal.

Cameron Buie
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