### 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 $x\in\mathbb{R}$.

# real-analysis

# analysis

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