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This was a homework question. I wasn't able to get far because I couldn't determine the properties of floor and ceiling functions. Any help would be awesome. $\def\lc{\left\lceil} \def\rc{\right\rceil}$ Here is the problem:

Show that $\lc \frac {2x + 1}{2} \rc - \lc \frac {2x + 1}{4} \rc + \lfloor \frac{2x+1}{4} \rfloor$ is always equal to either $\lc x \rc$ or $\lfloor x \rfloor$.

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Hint I see $4$ in the denominator and $2x$ in the numerator, so I would look at two cases: One, where $x$ is odd and two, where $x$ is even.

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