Subscript and Superscript: Level Change Indicators

You will remember that level-down and level-up indicators are used to indicate subscript or superscript, and that unless the current mode is uncontracted or numeric, the grade 1 indicator must be used.

Example:

9²

⠼⠊⠔⠼⠃

Vitamin B₃

⠠⠧⠊⠞⠁⠍⠔⠀⠠⠃⠰⠢⠼⠉

Note: a grade 1 indicator is required so that the phrase is not read as Vitamin Ben3.

As math expressions become more complicated, grade 1 indicators become more widely used.

Superscript (level up)	⠔
Subscript (level down)	⠢
Opening braille grouping symbol	⠣
Closing braille grouping symbol	⠜

You will remember that a level change indicator only applies to the one symbol that it precedes.

Example:

$x^{2} + yz$

⠭⠰⠔⠼⠃⠐⠖⠽⠵

When a subscript or superscript contains more than one symbol, braille grouping indicators must be used to identify where the level change begins and where it ends. These symbols do not occur in print. The grade 1 indicator is only used if the expression is not already in uncontracted mode.

Examples:

$x^{2 + y}z$

⠭⠰⠔⠰⠣⠼⠃⠐⠖⠽⠜⠵

If we analyze this, the "x" is not a stand-alone letter, so no grade 1 indicator is needed. The level change indicator reads as "in" until we change it to uncontracted. The change only applies to one symbol, so another grade 1 indicator is needed for the grouping symbol so that it isn't read as "gh". The numeric indicator sets numeric mode and uncontracted mode until it is broken by the space at the end of the expression, so no indicator is needed before the second grouping indicator.

Option: The grade 1 word indicator can also be used at the beginning of the expression.

x^2+yz

⠰⠰⠭⠔⠣⠼⠃⠐⠖⠽⠜⠵

More Examples:

$2 + n^{2 + m}$

⠼⠃⠐⠖⠝⠔⠣⠼⠃⠐⠖⠍⠜

Note: The number indicator sets uncontracted mode for the entire expression. The subscript expression is enclosed in braille grouping symbols.

$n^{m}$

⠝⠰⠔⠍

$n^{- m}$

⠰⠰⠝⠔⠣⠐⠤⠍⠜

Note: It is not a superscript negative sign, it is a superscript negative "m," so braille grouping symbols are required.

^-5+^-3

⠰⠔⠐⠤⠼⠑⠐⠖⠔⠐⠤⠼⠉

Note: The above example contains two superscript negative symbols. The grade 1 indicator is needed before the first level change indicator because the default mode is contracted. The numeric indicator sets numeric and uncontracted modes, so the grade 1 indicator is not needed with the second level change indicator.

Multiple Levels

A level change on a level change uses grouping symbols to clarify where each grouping symbol begins and ends.

$x_{y_{z}}$

⠰⠰⠭⠢⠣⠽⠢⠵⠜

$5^{y^{z}}$

⠼⠑⠔⠣⠽⠔⠵⠜

Note: The number 5 sets uncontracted mode throughout the remaining expression, so no grade 1 indicators are needed.

Although print uses superscript in ordinal numbers, braille does not. The numeric indicator sets uncontracted mode, so contractions are not used for "st" or "th.".

Example:

1^st 2^nd 3^rd 4^th

⠼⠁⠎⠞⠀⠼⠃⠝⠙⠀⠼⠉⠗⠙⠀⠼⠙⠞⠓

When an expression contains both subscript and superscript, subscript is listed first, followed by superscript.

$x_{z}^{y}$

⠭⠰⠢⠵⠰⠔⠽

When a subscript or superscript is written on the left side of an expression, the level change indicators precede the expression and subscript is listed first, followed by superscript.

Carbon-14: $_{6}^{14}C$

⠠⠉⠜⠃⠕⠝⠤⠼⠁⠙⠒⠀⠰⠢⠼⠋⠔⠼⠁⠙⠠⠉

Note: The grade 1 indicator is needed for the first level change. The numeric indicator then sets number and uncontracted mode, so the second level change indicator does not need a grade 1 indicator. The capital letter "C" is separated from the number by the capital indicator, so the grade 1 indicator is not needed in front of letter C.

Future FYI

In future units we will cover how level change indicators are used in complex fractions, radials, and other mathematical expressions. In the same way that braille grouping indicators identify an expression that appears in either subscript or superscript, other grouping indicators also identify the extent of the subscript or superscript expression. These are called an "item."

Definition on an "item" in UEB math

The following symbols are considered an "item" or a "group" and the level change indicator applies to the entire group or item:

An entire number
An expression enclosed in grouping symbols (fractions indicators, radical indicators, parenthesis, square brackets, curly braces, or braille grouping indicators)
An arrow or arbitrary shape

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