# Symbols:Brackets/Square Brackets

## Symbol

**Square brackets** are symbols used in a number of specific contexts.

They comprise the **left (square) bracket** $[$ and the **right (square) bracket** $]$.

The $\LaTeX$ code for \([\) is `[`

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The $\LaTeX$ code for \(]\) is `]`

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## Usage

**Square brackets** are used in the following contexts:

- To contain the argument for the image of a subset under a mapping: $f \sqbrk T := \set {\map f x: x \in T}$

This article is complete as far as it goes, but it could do with expansion.In particular: Plenty more usages, if only I could think of themYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

The $\LaTeX$ code for \(\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b\) is `\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b`

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The $\LaTeX$ code for \(f \sqbrk T\) is `f \sqbrk T`

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### Lowest Common Multiple: Deprecated Symbol

- $\sqbrk {a, b}$

The notation for the lowest common multiple is commonly seen as:

- $\sqbrk {a, b}$

However, as the $\sqbrk {a, b}$ notation is ambiguous, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(\sqbrk {a, b}\) is `\sqbrk {a, b}`

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### Closed Interval

- $\closedint a b$

The **closed interval between $a$ and $b$** is the set:

- $\closedint a b := a^\succcurlyeq \cap b^\preccurlyeq = \set {s \in S: \paren {a \preccurlyeq s} \land \paren {s \preccurlyeq b} }$

where:

- $a^\succcurlyeq$ denotes the upper closure of $a$
- $b^\preccurlyeq$ denotes the lower closure of $b$.

The $\LaTeX$ code for \(\closedint a b\) is `\closedint a b`

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### Closed Interval: Deprecated Symbol

- $\sqbrk {a, b}$

The notation for a closed interval is more commonly seen as:

- $\sqbrk {a, b} := \set {x \in S: a \le x \le b}$

However, as the $\sqbrk {a, b}$ notation is ambiguous, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(\sqbrk {a, b}\) is `\sqbrk {a, b}`

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### Right Half-Open Interval

- $\hointr a b$

The **right half-open interval between $a$ and $b$** is the set:

- $\hointr a b := a^\succcurlyeq \cap b^\prec = \set {s \in S: \paren {a \preccurlyeq s} \land \paren {s \prec b} }$

where:

- $a^\succcurlyeq$ denotes the upper closure of $a$
- $b^\prec$ denotes the strict lower closure of $b$.

The $\LaTeX$ code for \(\hointr a b\) is `\hointr a b`

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### Right Half-Open Interval: Deprecated Symbol

- $\left [{a, b}\right)$

The notation for a right half-open interval is more commonly seen as:

- $\left [{a, b}\right) := \set {x \in S: a \le x < b}$

However, for consistency with other interval notation, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(\left [{a, b}\right)\) is `\left [{a, b}\right)`

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### Half-Open Interval to the Left

- $\hointl a b$

The **left half-open interval between $a$ and $b$** is the set:

- $\hointl a b := a^\succ \cap b^\preccurlyeq = \set {s \in S: \paren {a \prec s} \land \paren {s \preccurlyeq b} }$

where:

- $a^\succ$ denotes the strict upper closure of $a$
- $b^\preccurlyeq$ denotes the lower closure of $b$.

The $\LaTeX$ code for \(\hointl a b\) is `\hointl a b`

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### Left Half-Open Interval: Deprecated Symbol

- $\left ({a, b}\right]$

The notation for a left half-open interval is more commonly seen as:

- $\left ({a, b}\right] := \set {x \in S: a < x \le b}$

However, for consistency with other interval notation, its use is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.

The $\LaTeX$ code for \(\left ({a, b}\right]\) is `\left ({a, b}\right]`

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