In Nemeth Code, numbers are written using lower signs. In some situations, they are not preceded by a number sign (dots 3-4-5-6).
There is ambiguity between punctuation and numbers. When in doubt, a numeric indicator is used to show that something is a number. Dots 4-5-6 is the punctuation indicator. It is used to show that punctuation is being used (when in a math context).
A plus sign is the "ing" sign, a minus sign is the braille hyphen. The equals sign is space, dots 4-6, dots 1-3, space.
Fractions are easy. The start of the fraction is marked with the "th" sign, the fraction line is the "st" sign, and the end of the fraction is marked with the number or "ble" sign.
You can also have fractions of fractions (complex fractions). The larger fraction elements are marked with a dot 6. The smaller fraction elements are not.
You can also have fractions of fraction of fractions. These are called hypercomplex fractions. The major elements are marked with a double dot 6. The rest are as above.
A Greek letter is marked with dots 4-6. A square root starts with dot 3-4-5 (the "ar" sign), and ends with dots 1-2-4-5-6 (the "er" sign).
This index is arranged in "transcriber order". This order gives a number from 1 to 63 to all the braille cells. Here is the order:
The letters a-z (excluding w). The letter w is listed as cell 40.
The "and" sign means factorial in a math context. In inkprint this is written as an exclamation mark. For example, 6! is written as #6& in Nemeth Code.
If preceded by a dots 4-6, the "and" sign means the Greek letter chi.
The "for" sign means general omission sign. In arithmetic problems, the general omission symbol shows what the reader is expected to calculate. Often shown as a question mark in inkprint. For example, 2+3=? would be written as #2+3 .k = in Nemeth Code.
The "of" sign means a left parenthesis in Nemeth Code. It is used in both a math and a literary context. The right parenthesis is a "with" sign. The dropped "g" parenthesis are not used in Nemeth Code at all.
The "the" sign means integral in Nemeth Code. This basic symbol in calculus is shown as a tall stylized S. The integral of x dx is written as !x dx in Nemeth Code.
The "with" sign means a right parenthesis in Nemeth Code. It is used in both a math and a literary context. The left parenthesis is an "of" sign. The dropped "g" parenthesis are not used in Nemeth Code at all.
The "ch" sign means times or centered dot in Nemeth Code. The centered dot is used to show multiplication in algebra (were the x used in arithmetic might be confused with the letter x). Five times x might be written as #5x or #5*x in Nemeth Code, depending on whether the inkprint shows a centered dot or not.
The "gh" sign is a bit tricky. If there is a multipurpose indicator (a dot 5) starting off an expression, then the presence of the "gh" sign means that the next portion is placed above the first expression. Without a multi-purpose indicator, then "gh" signals an index of radical (such as a cube root).
Here are the two structures: (gh) index (ar) root (er) for a radical with an index of radical; or (dot 5) base expression (gh) over expression (er). In both structures, the "er" sign terminates the expression. To write the cube root of 64, write <#3>#27] in Nemeth Code. To write an 8 above an x, write "x<#8] in Nemeth Code.
The "sh" sign means to place underneath the base expression. Its use is symmetrical with the "gh" (when the "gh" means above). To write a 6 below an x, write "x%#6] in Nemeth Code.
The "th" sign means start a simple fraction. A fraction starts with the "th" sign, uses the "st" sign for the fraction line, and the "ble" or number sign to close the fraction.
When a dot 6 precedes the "th" sign, it means that you are looking at a complex fraction, or a fraction of a fraction. In that case dot 6 elements are the most significant. To write the complex fraction of the fraction x over 3 all over the fraction 4 over 5, write ,??x/3#,/?4/5#,# in Nemeth Code. Notice that the number sign is not used to show numbers inside the fraction.
If there are dot 6, dot 6, it means you have a hypercomplex fraction (a fraction of a fraction of a fraction).
The "wh" sign means a horizontal bar. To write x with an overbar, write x: in Nemeth Code. To write xyz with an overbar, write "xyz<:} in Nemeth Code.
There are also a small number of obscre symbols starting with the "wh" sign, such as :"k (bar over less than sign) and :.1 (bar over greater than sign).
The "ed" sign is used to show special shapes in Nemeth Code. If you look at the index of the Nemeth Code, you will see a very long list of symbols that start with the "ed" sign. The most common are:
$c circle
$i intersecting lines
$p is perpendicular to
$s star
$t triangle
The "er" sign is the termination indicator. It ends a radical. It also ends above or below constructs.
The "ou" sign is a vertical bar. The vertical bar is used for many different things in inkprint, so this symbol is used in many different contexts. The most common is for absolute value. To write the absolute value of minus 4 is 4 in Nemeth Code, write \-4\ .k #4.
The "ow" sign is used for a comma located at the subscript or superscript level. In practice, it is usually used just at the subscript level. To write x sub i comma j, write x;i[j in Nemeth Code.
Cell 40 is the letter w. It is out of order since Louis Braille was French, and the French despised the letter w.
Cell 41 is the dropped a. In Nemeth Code, this is ambiguous. It is either the numeral 1 or the literary comma. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 42 is the dropped b. In Nemeth Code, this is ambiguous. It is either the numeral 2 or the semicolon. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 43 is the dropped c. In Nemeth Code, this is ambiguous. It is either the numeral 3 or the colon. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 44 is the dropped d. In Nemeth Code, this is ambiguous. It is either the numeral 4 or the literary period. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 41 is the dropped e. In Nemeth Code, this is the numeral 5.
Cell 46 is the dropped f. In Nemeth Code, this is ambiguous. It is either the numeral 6 or the literary exclamation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 47 is the dropped g. In Nemeth Code, this is the numeral 7.
Cell 48 is the dropped h. In Nemeth Code, this is ambiguous. It is either the numeral 8 or the literary quotation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 49 is the dropped i. In Nemeth Code, this is ambiguous. It is either the numeral 9 or the "in" sign.
Cell 50 is the dropped j. In Nemeth Code, this is ambiguous. It is either the numeral 0 or the literary quotation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 51 is the "st" sign. In Nemeth Code, it is the horizontal simple fraction line (the part of the fraction that separates the top part from the bottom part).
When a sign of comparison is negated by a superimposed slash or vertical bar, show it with the "st" sign. For example, the parallel sign is $l and the perpendicular sign is $p. The sign for not perpendicular is /$p and the sign for not parallel is /$l.
Cell 52 is the "ing" sign. In Nemeth Code it means plus. When followed by a minus (dots 3-6), it means "plus or minus". If you need to write "a plus followed by a minus", separate them with a dot 5 as: +"-
Cell 53 is the "ble" sign. It means closing fraction or the numeric indicator. To write 1 minus the fraction 1 over 3, write #1-?1/3# (the numeric indicator is not used inside the fraction. The first "ble" sign shows that you have the number 1. The second "ble" sign closes the fraction.
Cell 54 is the "ar" sign. It starts off a radical or square root. To write the square root of x+3, write >x+3] in Nemeth Code. Notice how the "er" sign terminates the radical.
Cell 55 is dot 3. In Nemeth Code it is the apostrophe or prime. To write x prime, write x' in Nemeth Code. Three dot 3's in a row are an ellipsis, just like in literary braille.
Cell 56 is dots 3-6. In Nemeth code, cell 56 is either a hyphen or a minus sign. Two dots 3-6 means a short dash, 4 dots 3-6 means a long dash.
Dots 3-6 followed by an "ing" sign means a minus or a plus (in inkprint a minus right over a plus sign). To show that a minus sign followed by a plus sign, insert a dot 5 between then, as -"+.
Cell 57 is the dot 4. The dot 4 is used to produce a huge array or special symbols. It is used for a script type, for German letters. Dot 4 s means dollar sign, dot 4 l is a pound Sterling (English currency) symbol. The list is most extensive. Please look at the Nemeth Code index for the complete list.
Cell 58 is dots 4-5. It is the superscript indicator. To write x squared plus y squared, write x^2"+y^2 in Nemeth Code. Notice that dot 5 or a space takes you back to the baseline. To write e raised to the x squared power, write e^x^^2 in Nemeth Code. Be aware that Nemeth code supports 7 different levels of superscript. While you may never have seen a subscript of a superscript of a superscript, it is nice to know that it is supported in Nemeth Code. See Cell 62, dots 5-6 for information about subscripts.
Cell 59 is dots 4-5-6. Lots of symbols start with dots 4-5-6. Remember that dots 4-5-6 is the punctuation indicator. Here is a small list:
_l identity
_/ slash
_* backslash
_< caret
_] dagger
_0 empty set
See the Code Book for Nemeth for the full list of symbols.
Cell 60 is dot 5. Dot 5 is called the "multipurpose indicator" in Nemeth Code. It is used to show that a superscript or a subscript is over, that text is going back to the baseline. Between a letter and a number, the dot is used to show that the number is not a subscript (in Nemeth Code, a number right after a letter is presumed to be a subscript). A dot 5 is used to start of an expression modified by something above or below it.
There are also a large number of symbols that start with dot 5. Here is a partial list:
"k less than
"k: less than with an underbar
"k.k less than or equal
Cell 61 is dots 4-6. Inside a number, dots 4-6 is the decimal point. Dots 4-6 before a letter is a Greek letter indicator. Dots 4-6, dots 5-6 before a letter is italics. Please note that .k is the equals sign. In Nemeth Code, you need a space on either side. So there is potential ambiguity between an equal sign and the Greek kappa.
There are various other math symbols that start with dots 4-6. Here is a partial list:
.( left curly brace
.) right curly brace
..( left angle bracket
..) right angle bracket
.* degree sign or hollow dot
.% intersection sign (cap)
.+ union sign (cup)
.# number sign
Cell 62 is dots 5-6, the subscript sign. To write x sub i comma j baseline plus 5, write x_i[j"+5 in Nemeth Code. Notice that dot 5 or a space takes you back to the baseline. To write x sub i sub sub 2, write x_i__2 in Nemeth Code. Be aware that Nemeth code supports 7 different levels of subscript. While you may never have seen a subscript of a subscript of a superscript, it is nice to know that it is supported in Nemeth Code. See Cell 58, dots 4-5 for information about superscripts.
Dots 5-6 is also the English letter indicator. It is used to make the distinction between an italics letter b and the Greek letter b. The presence of dots 5-6 tells you that it is not a Greek letter.
Cell 63 is dot 6, the capitalization indicator. It is also the mathematical comma. By mathematical comma, we mean a comma at the superscript or subscript level. For example, in the expression x sub i, j the comma between i and j is done with a dot 6.
A double dot 6 is either a whole word capitalized or a Hebrew letter. Since Hebrew letters are rare in mathematics, this should not present a problem.
The capital sign is used to show the difference between simple fractions and complex fractions. The double capital sign is used to show the difference between complex fractions and hypercomplex fractions.
In addition, a considerable signs start with dot 6. Here is a partial list:
,= infinity
,( left enlarged parenthesis
,) right enlarged parenthesis
,* therefore
,' ditto mark