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Let $x,y \in \Bbb R$ and $xby \Leftrightarrow \exists k\in \Bbb Z \ tg(x)+k=tg(y)$.

Find $[x]_b$.

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Any ideas ,self work, insights...? And try not to write as if you were giving orders. – DonAntonio Jan 14 at 21:11
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It's not clear to me that there's any way to write the result nicer than the obvious $\{\tan^{-1}(\tan(x)+k)+\pi m \mid k,m\in \mathbb Z\}$... – Henning Makholm Jan 14 at 21:12
@DonAntonio: That should be "And try not to write questions that look like just a quote of a homework assignment without any thoughts of your own" -- the cute phrasing about "giving orders" is a red herring that just confuses those who need the advice most. – Henning Makholm Jan 14 at 21:15
Well, I might've formulated my question in a more mannered way but I thought that it's fine. Anyway, thanks Mr. Makholm for your help. – Max Jan 14 at 21:29
@HenningMakholm, I can'y understand what red herring you see in my innocent but direct and, as far as I can see, crystal clear phrase. I don't really care whether the question is from homework or not for this matter, but for manners. – DonAntonio Jan 15 at 2:55

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