Prove or disprove each of these statements about the floor and ceiling functions. $\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rfloor$ for all real number $x.$ $\left \lfloor 2x \right \rfloor = 2\left \lfloor x \right \rfloor$ whenever $x$ is a ... $x$ and $y.$ $\left \lceil x/2 \right \rceil = \left \lfloor x+1 / 2 \right \rfloor$ for all real numbers $x.$

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Apr 11, 2019
in Set Theory & Algebra
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