Franklin's Notes

Integral and fractional parts

For $x\in\mathbb R$, the integral part of $x$, denoted $[x]$ or $\lfloor x\rfloor$, is defined as the largest integer less than or equal to $x$. The fractional part of $x$, denoted ${x}$, is defined as $x$ modulo $1$, or $x-[x]$. Note that $[x]+{x}=x$ for any $x\in\mathbb{R}$.