床関数・天井関数

\[\left\lfloor \frac{n}{2}\right\rfloor +\left\lceil \frac{n}{2}\right\rceil =n\]

\[\left\lceil z\right\rceil -\left\lfloor z\right\rfloor =\sgn\mod\left(\Re z,1\right)+i\sgn\mod\left(\Im z,1\right)\]

\[\left\lceil z\right\rceil =-\left\lfloor -z\right\rfloor \]

\[\left\lfloor z\right\rfloor =z-\mod\left(z,1\right)\]

\[\left\lfloor x\right\rfloor =\max\left\{ n\in\mathbb{Z};n\leq x\right\} \]