Sqb1

Summary

Sometimes used as a synonym of $(\square)$ for avoiding nested parentheses.

Equivalence class: given an equivalence relation, $[x]$ often denotes the equivalence class of the element $x$.

Integral part: if $x$ is a real number, $[x]$ often denotes the integral part or truncation of $x$, that is, the integer obtained by removing all digits after the decimal mark. This notation has also been used for other variants of floor and ceiling functions.

Iverson bracket: if $P$ is a predicate, $[P]$ may denote the Iverson bracket, that is the function that takes the value $1$ for the values of the free variables in $P$ for which $P$ is true, and takes the value $0$ otherwise. For example, $[x=y]$ is the Kronecker delta function, which equals one if $x=y$, and zero otherwise.

In combinatorics or computer science, sometimes $[n]$ with $n\in\mathbb{N}$ denotes the set $\{1,2,3,\ldots,n\}$ of positive integers up to $n$, with $[0]=\emptyset$.