床関数と天井関数の定義

(1)床関数の定義

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

(2)複素数の床関数

\[ \left\lfloor z\right\rfloor =\left\lfloor \Re z+i\Im z\right\rfloor =\left\lfloor \Re z\right\rfloor +i\left\lfloor \Im z\right\rfloor \]

(3)天井関数の定義

\[ \left\lceil x\right\rceil =\min\left\{ n\in\mathbb{Z};x\leq n\right\} \]

(4)複素数の天井関数

\[ \left\lceil z\right\rceil =\left\lceil \Re z+i\Im z\right\rceil =\left\lceil \Re z\right\rceil +i\left\lceil \Im z\right\rceil \]