• First posted August 9, 2001.
• Rev. 1 Reference number element added. Aug. 10, 2001.

### Numbers, the Number Sign and the Numeric Indicator

#### Introduction.

This discussion is an attempt to formalize the existing logical structure surrounding the use of the Numeric Indicator according to §7-12 of Rule II. of the Nemeth Code with some amplification from other rules. The rules for numbers in non-decimal bases and for numbers in Tables and Diagrams are not covered here.

The intent is to provide some information that might be a useful start to defining a DTD or some sort of Schema for Nemeth. References in brackets are to the Nemeth Code.

#### Numbers.

A literary number is as defined in the English Braille Code and is not discussed here.

A Nemeth number used in technical material is based on the Nemeth numerical symbols. These include the Nemeth numeral cells (0-9 in Braille ASCII), the decimal point (. in Braille ASCII), and any embedded mathematical commas (, in Braille ASCII) or spaces used for grouping digits. Note that a mathematical comma used for grouping is never followed by a space; this rule serves to distinguish the mathematical comma used as a numerical symbol from one used as punctuation since it must be followed by a space in the latter context. A number, with or without grouping symbols, is always mathematical context.

[Rule II, §7-8] According to the scheme that I am proposing, a number, per se, could only be a child element of one of the four proposed number elements:

1. The plain number element, PNE, is simply a wrapper for a Nemeth number like the `<mn>` element
2. An alignment number element, ANE, is a Nemeth number preceded by an ANI
3. An indicated number element, INE, is a Nemeth number preceded by a CNI
4. A reference number element, RNE, is a Nemeth number preceded by an RNI

#### Number sign and Numeric Indicator (NI).

The physical cell dots 3-4-5-6 or Braille ASCII # is genererally called the number sign in literary braille and the Numeric Indicator (NI) in Nemeth. This cell has four semantic forms related to its use with numerals. It is also used as part of the closing fraction indicators as specified in Rule XII.

LNS
Literary number sign (LNS) as used before literary numbers
ANI
The Nemeth Alignment Numeric Indicator (ANI) is the name proposed here for the Numeric Indicator when used to ensure recognition of the lower-cell position of Nemeth numbers
CNI
The Nemeth Change-of-Semantics Number Indicator (CNI) is the name proposed for the Numeric Indicator when used to ensure distinction of a Nemeth number from the same cells used as punctuation
RNI
The Nemeth Reference Number Indicator (RNI) is the name proposed for the Numeric Indicator when used to ensure differentiation of a Nemeth number used as a label following a reference symbol[Rule VII] from a Nemeth number used as the second operand of the same symbol functioning as a binary operator.[Rule XIX] This element is also used after the interior shape modification indicator to indicate a numeral embedded in a shape.

#### Useage Rules for Number Elements.

See elsewhere for the use of the literary numbers.

These are the rules for the use of the four number elements that use Nemeth numbers:

1. The ANE or alignment number element is only used immediately following a numerical break or numbreak. An ANI thus defined can be used in either a text or mathematical context.
2. The INE or indicated number element is only used immediately a literary break or litbreak. An INE as thus defined can only be used at the start of a mathematical context immediately preceded by a text context.
3. The RNE or reference number element is only used in references according to Rule VII [Cf. 9d] and following an interior shape-modification indicator[9e]
4. The PNE or plain number element is used in all other contexts.

#### Glossary.

A numerical break or numbreak is one of the following:

• a spacingbreak with three exceptions
• a pretty-printing space or space, minus sign occurring in a problem arranged for computation or a set of equations arranged so as to align equals marks [11b] is not a numbreak
• a space used as a grouping aid to partition a numeral into segments is considered to be a numerical symbol and is not a numbreak [11c]
• a space that is part of the mathematical comma, space separator element used in an enclosed list [10] is not a numbreak
• an enlarged open grouping symbol or the same followed by a minus sign used at the start of each line of a determinant or matrix [9c]
• a start symbol for transcriber's notes[9g]

A spacing break or spacingbreak [9a] is one of the following:

• a space
• a line break,
• a space, minus sign sequence
• a line break, minus sign sequence

A literary break or litbreak is one of the following:

The literary punctuation subset is comprised of the following cells:

The special literary punctuation subset is comprised of the cells with the following semantics. These semantic cells are always preceded by a punctuation indicator in a mathematical context to distinguish them from the same physical cells being used as numerals.

• a colon
• a semi-colon
• an open or close single or double quote (the symbols for the single quotes are not the same physical symbol as that used for an apostrophe)
• a literary period (which is not the same physical cell that is used for the decimal point)
• a literary exclamation mark (which is not the same physical cell that is used for the factorial sign),
• a question mark (which is not the same physical cell that is used for the omission symbol)

The dual-use literary punctuation mark subset is comprised of the dual-use physical symbols when used within or immediately following a literary (non-mathematical) context.

• a literary short or long dash (but not when these same cells are used as mathematical dashes)
• a literary hyphen (but not when this same cell is used as a mathematical hyphen)
• a literary ellipsis (but not when these same cells are used as a mathematical ellipsis)

#### Notes.

##### Use of the Plain Number Element.

A PNE is used in any context where an ANE or INE is not mandated. [11e] This includes but is not limited to

• a number used as an item in enclosed list [11a]
• a numeral that is the first character of an item in an enclosed list [11a]
• a problem arranged spatially for computation or a set of equations arranged so as to align equals marks [11b]
• a number preceded by a space used to group numerals (e.g. #1 000 001) [11c]
• following numerical punctuation including a dual-use numerical punctuation mark such as a numerical hyphen or ellipsis [11d] or a sign of grouping
• a number in a mathematical expression that is not preceded by a space

##### Aside on numerical punctuation.

According to the Nemeth rules, a punctuation mark from the special literary set defined here requires a preceding punctuation indicator in a mathematical context. This will be discussed elsewhere. Punctuation marks that are not in the special literary punctuation subset are treated as follows when used with numerals.

Comma. According to the Nemeth rules, the mathematical comma, which must generally be followed by a space, is used rather than the literary comma immediately following a Nemeth numeral. The mathematical comma is a physically different cell from the literary comma. An NI is not needed immediately following a mathematical comma; the rules for the use of the NI following a space are covered by the rules for a numerical break.

Hyphen, dashes, ellipsis. According to the Nemeth rules, these dual-use punctuation marks are mathematical, rather than literary, punctuation marks when used directly between or immediately following Nemeth numbers (or other mathematical expressions) and thus do not require the use of the CNI to effect a change of semantics. A range would be transcribed as for example, #1-3, whereas a time of day would be transcribed as for example, #2_:#45 where the underscore is the Braille ASCII for the punctuation indicator needed before the colon.

Apostrophe-ess. According to the Nemeth rules, an ordinal ending or a plural or possessive ending, whether or not preceded by an apostrophe (with its required preceding punctuation indicator), that follows a Nemeth number does not effect a change of semantics and is always a mathematical expression. In the unlikely situation of a Nemeth number immediately such a construct, an NI wouldn't be used since this would be neither a literary break nor a numerical break.