# Lesson 9.0: Subscripts

## Symbols

$\text{level change down indicator (subscript)}$

⠢

$\text{braille grouping, opening}$

⠣

$\text{braille grouping, closing}$

⠜

## 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 entire radical expression, enclosed in radical 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.

Grade 1 mode is turned on by grade 1 indicators and by the numeric indicator. When grade 1 mode is turned on by the numeric indicator, it is turned off by a space, hyphen, or dash.

## Explanation

A quantity displayed below the normal line of text and generally in a smaller point size is known as a subscript. Subscripts are commonly used to indicate indices, including the entry in a matrix (row and column) and a range of other operations and notations.

The level change down indicator is used in braille to identify an item in the subscript position. The UEB definition of item was introduced in an earlier lesson. When the material in the subscript position extends beyond an item, it must be enclosed in braille grouping indicators. The level change down indicator is dots two six. The opening braille grouping symbol is dots one two six and the closing braille grouping symbol is dots three four five. All three symbols also have a grade 2 meaning therefore the symbols must be in grade 1 mode. Grade 1 mode is set by the numeric indicator or by grade 1 indicators.

The value is written first followed by the level change indicator and the item in the subscript position. If the item in the subscript position appears to the left of the value, the subscript indicator must precede the value with a grade 1 indicator unless grade 1 mode is already in effect.

The level change down indicator terminates numeric mode. The numeric indicator must be used with a numeral that appears in the subscript position.

When a subscript has multiple levels (a subscript of a subscript), braille grouping indicators must be used with the level change indicators.

When a value has both a subscript and superscript (exponent), work from bottom to top or left to right unless print indicates a different sequence of subscript/superscript items.

### Example 1

${x}_{y}$

⠭⠰⠢⠽

### Example 2

${3}_{x}$

⠼⠉⠢⠭

### Example 3

${x}_{2y}$

⠭⠰⠢⠣⠼⠃⠽⠜

### Example 4

${3}_{2}$

⠼⠉⠢⠼⠃

### Example 5

${x}_{{a}_{b}}$

⠰⠰⠭⠢⠣⠁⠢⠃⠜

### Example 6

${4}_{{x}_{3}+3}$

⠼⠙⠢⠣⠭⠢⠼⠉⠐⠖⠼⠉⠜

### Example 7

${4}_{{x}_{3}}+3$

⠼⠙⠢⠣⠭⠢⠼⠉⠜⠐⠖⠼⠉

### Example 8

${y}_{2}-y$

⠽⠰⠢⠼⠃⠐⠤⠽

### Example 9

${B}_{12}$

⠠⠃⠰⠢⠼⠁⠃

### Example 10

$C{O}_{2}$

⠠⠠⠉⠕⠰⠢⠼⠃

### Example 11

${x}_{1}+{x}_{2}$

⠰⠰⠭⠢⠼⠁⠐⠖⠭⠢⠼⠃

### Example 12

${y}_{{x}^{2}}$

⠰⠰⠽⠢⠣⠭⠔⠼⠃⠜

### Example 13

${a}_{{1}^{2}}$

⠰⠰⠁⠢⠣⠼⠁⠔⠼⠃⠜

### Example 14

${}_{x}{}^{}n_{}^{}$

⠰⠢⠭⠝

### Example 15

${}_{2}{}^{}x_{}^{}$

⠰⠢⠼⠃⠭

### Example 16

$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]$

⠰⠰⠰⠠⠨⠣⠁⠢⠼⠁⠁⠀⠁⠢⠼⠁⠃⠠⠨⠜

⠀⠀⠀⠠⠨⠣⠁⠢⠼⠃⠁⠀⠁⠢⠼⠃⠃⠠⠨⠜⠰⠄