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# Lesson 6.3: Brackets and Braces

## Symbols

$\left[\phantom{\rule{.3em}{0ex}}\text{opening square brackets}$
⠨⠣

$\right]\phantom{\rule{.3em}{0ex}}\text{closing square brackets}$
⠨⠜

$\left\{\phantom{\rule{.3em}{0ex}}\text{opening curly braces}$
⠸⠣

$\right\}\phantom{\rule{.3em}{0ex}}\text{closing curly braces}$
⠸⠜

## Review

There are indicators in UEB that apply to the item appearing just before or after the indicator. An item is defined as any one of the following groupings if they appear in the position affected by the indicator:

• An entire number, i.e. the initiating numeric symbol and all succeeding symbols within the numeric mode thus established (which would include any interior decimal points, commas, separator spaces, or simple numeric fraction lines).
• An entire general fraction, enclosed in fraction indicators.
• An arrow.
• An arbitrary shape.
• Any expression enclosed in matching pairs of round parentheses, square brackets or curly braces.
• Any expression enclosed in the braille grouping indicators.
• If none of the foregoing apply, the item is simply the next individual symbol.

## Explanation

Brackets and braces used in mathematics are the same symbols used in literary text. Brackets and braces in braille are formed with two cells; a prefix that distinguishes the type of bracket (square or curly) and the root that defines the symbol as opening or closing. The prefix for square brackets is dots four six and the prefix for curly brackets (braces) is dots four five six. The root symbol for opening is dots one two six and the root symbol for closing is dots three four five.

Braces and brackets are used in many different contexts in math. They are used in complex expressions in addition to or in place of parentheses. Brackets are often used in grouping. Different kinds of brackets can be used to show multiple levels of grouping within an expression. They are also used to denote least common multiple and in interval notation they can be used to show that a range of values includes a certain value. Braces are often used to indicate set notation.

A single letter that appears within opening and closing brackets or braces is considered to be standing alone and a grade 1 indicator is needed. Brackets and braces terminate numeric mode. The numeric indicator must be used with a digit that immediately follows a bracket or brace. Follow print for spacing and punctuation.

### Example 1

$\left[8-\left(6÷3\right)\right]$
⠨⠣⠼⠓⠐⠤⠐⠣⠼⠋⠐⠌⠼⠉⠐⠜⠨⠜

### Example 2

$\left[-6,2\right]$
⠨⠣⠐⠤⠼⠋⠂⠀⠼⠃⠨⠜

### Example 3

$\left[-5,3\right)$
⠨⠣⠐⠤⠼⠑⠂⠀⠼⠉⠐⠜

### Example 4

$B=\left\{-1,2,4.4\right\}$
⠰⠠⠃⠀⠐⠶⠀⠸⠣⠐⠤⠼⠁⠂⠀⠼⠃⠂⠀⠼⠙⠲⠙⠸⠜

Remember that you should reduce the number of indicators used within equations. That is why it is typically best when reading mathematical expressions with multiple interruptions to use grade one passage indicators. They are less intrusive than using interior indicators for every interruption.

### Example 5

$A=\left\{x|x=4y\right\}$
⠰⠰⠰⠠⠁⠀⠐⠶⠀⠸⠣⠭⠀⠸⠳⠀⠭⠀⠐⠶⠀⠼⠙⠽⠸⠜⠰⠄

### Example 6

$\left\{5,-1,2,m,p,B\right\}$
⠰⠰⠰⠸⠣⠼⠑⠂⠀⠐⠤⠼⠁⠂⠀⠼⠃⠂⠀⠍⠂⠀⠏⠂⠀⠠⠃⠸⠜⠰⠄

### Example 7

$\left\{0\right\}$
⠸⠣⠼⠚⠸⠜

### Example 8

$\left\{y\right\}$
⠸⠣⠰⠽⠸⠜

### Example 9

$\left\{y=z\right\}$
⠸⠣⠰⠽⠀⠐⠶⠀⠰⠵⠸⠜

### Example 10

$\left\{\right\}$
⠸⠣⠀⠸⠜