Find all real numbers $x$ satisfying:
a. $\lfloor x + 1/2 \rfloor = \lfloor x \rfloor$.
b. $\lfloor x + 1/2 \rfloor = \lceil x \rceil$.
Finding $x$ such that $\lfloor x + 1/2 \rfloor = \lfloor x \rfloor$
2
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elementary-number-theory
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0Begin with a few examples, such as $x = 1$, $x=1.2$, $x=1.5$, $x=1.7$, etc. Try to spot the pattern. – 2012-08-10
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0First, consider a positive $x.$ Write $x$ as $k + f$ where $k$ is an integer, and $f$ is a real number between $0$ and $1$. – 2012-08-11