The purpose of this database is to allow individuals to look up Nemeth symbols and math related concepts, using the words they are used to hearing. These symbols and concepts are listed at the beginning of the page. Once you have found what you are looking for in the list, select that particular link, which will take you to a description of how the symbol or concept is written in Nemeth code. At the end of the description, you will find three additional links to examples in Nemeth code. The first link takes you to a brf file that includes examples using Nemeth code in English Braille American Edition (EBAE). The second link takes you to a brf file that includes examples using Nemeth code within Unified English Braille (UEB) contexts. The third link takes you to a Microsoft Word document that includes examples in print and SimBraille. We will continue to build this database and would welcome any comments or suggestions you might have for improving this database.

Sara Larkin, Susan Osterhaus, and Tina Herzberg

Math Terms

Definitions

Alpha is a Greek letter. The lowercase form of this letter is often used to represent an angle measure. To write Alpha in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "a" (dot 1). When writing this immediately after a trigonometric function such as sin, cos, tan, csc, sec, or cot, include a space before the Greek letter indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Angle brackets are a type of grouping symbol. They are commonly used when writing vector notation in component form. The opening angle bracket is dots 4-6 written twice in front of the "of" contraction (dots 1-2-3-5-6). The closing angle bracket is dots 4-6 written twice in front of the "with" contraction (dots 2-3-4-5-6). The numeric indicator is not used inside grouping symbols such as the angle brackets. See vectors for more Nemeth code related to vectors. The sample document includes vector notation as well as the angle brackets used in component form. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The antiderivative of a function is denoted by the capital letter of that function name followed by the letter x in parentheses. The opening parenthesis is the "of" contraction (dots 1-2-3-5-6) and the closing parenthesis is the "with" contraction (dots 2-3-4-5-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Arcs are denoted using the five step rule. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified, which should be two capital letters for a minor arc or three capital letters for a major arc. The capitalization indicator must be placed before each capitalized letter since each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction (dots 1-2-6). Think "high" which also uses the "gh" contraction. Step 4: Write the modifier which is the arc symbol. It is the shape indicator (dots 1-2-4-6) followed by the letter a (dot 1) for arc. Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Beta is a Greek letter. The lowercase form of this letter is often used to represent an angle measure. To write Beta in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "b" (dots 1-2). When writing this immediately after a trigonometric function such as sin, cos, tan, csc, sec, or cot, include a space before the Greek letter indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The binomial coefficient which is used in probability and the binomial theorem is written with parentheses and read "n choose r" where n and r are two numbers written vertically in print. Remember the open and closed parentheses are the same as the "of" (dots 1-2-3-5-6) and "with" (dots 2-3-4-5-6) contractions respectively. The directly under indicator is also used in this notation. It is the "sh" contraction (dots 1-4-6). Think of the word "shallow" which has the "sh" contraction as being a way to put something under (or in a shallow position to) something else. This is used between the numbers that appear on the first line and the second line in print. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Braces, sometimes called curly brackets, are a type of grouping symbol. They are used as a third level of parentheses or for set notation. The opening brace is dots 4-6 in front of the "of" contraction (dots 1-2-3-5-6). The closing brace is dots 4-6 in front of the "with" contraction (dots 2-3-4-5-6). The numeric indicator is not used inside grouping symbols such as braces. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Brackets are a type of grouping symbol. They are used as a second level of parentheses or for the integer function. Note that brackets are not always used in pairs. The closing right bracket is commonly used in the process of calculating definite integrals in calculus. The opening bracket is a dot 4 in front of the "of" contraction (dots 1-2-3-5-6). The closing bracket is a dot 4 in front of the "with" contraction (dots 2-3-4-5-6). The numeric indicator is not used inside grouping symbols such as brackets. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Combinations which are read n choose r can be written several different ways. Method 1: capital c followed by n comma r inside a set of parentheses which are the "of" (dots 1-2-3-5-6) and "with" (dots 2-3-4-5-6) contractions. Method 2: capital c followed by the subscript indicator (dots 5-6) n comma r. Method 3: subscript indicator (dots 5-6) n capital c r. If r is a number, no subscript is needed before it, but if it is a variable, the subscript indicator is needed before it. Method 4: parentheses with r below n. Remember the open and closed parentheses are the same as the "of" (dots 1-2-3-5-6) and "with" (dots 2-3-4-5-6) contractions respectively. The directly under indicator is also used in this notation. It is the "sh" contraction (dots 1-4-6). Think of the word shallow which has the "sh" contraction as being a way to put something under (or in a shallow position to) something else. This is used between the first line which represents n and the second line which represents r. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The definite integral is an integral over a certain interval. It starts with the integral sign which is dots 2-3-4-6. Then it is followed by a subscript indicator (dots 5-6) and the starting value of the interval. Next is the superscript indicator (dots 4-5) and the ending value of the interval. Finally the baseline indicator (dot 5) followed by the function and then dx. On occasion, the interval values are directly over or directly under instead of just raised and lowered. In this case the five step rule is used which starts with the multipurpose indicator (dot 5) and ends with the termination indicator (dots 1-2-4-5-6) instead of the baseline indicator. Also the directly under indicator (dots 1-4-6) is used instead of the subscript indicator and the directly over indicator (dots 1-2-6) is used instead of the superscript indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Degrees can be used to specify an angle or arc measure, to write degrees Fahrenheit, and to write degrees Celsius or Centigrade. The degree symbol is actually three cells long. It begins with the superscript indicator (dots 4-5), since it is raised, followed by the two-cell hollow dot symbol (dots 4-6 and then dots 1-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Delta is a Greek letter. The lowercase form of this letter is often used to represent a small change in the value of a variable in calculus. To write Delta in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "d" (dots 1-4-5). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Delta is a Greek letter. The uppercase form of Delta is most often used to represent the change in something. To write Delta in Nemeth code, begin with a Greek letter indicator (dots 4-6) followed by the capital indicator (dot 6) and then by the letter "d" (dots 1-4-5). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The derivative of y with respect to x is written as a simple fraction which starts with an opening fraction indicator which is the “th” contraction (dots 1-4-5-6) followed by “dy”, then uses the slash which is the “st” contraction (dots 3-4) followed by “dx”, and finishes with the closing fraction indicator (dots 3-4-5-6). For the 2nd, 3rd, or other derivatives of y with respect to x, the superscript indicator (dots 4-5) is used to raise the 2, 3, etc. along with the baseline indicator (dot 5) after the 2, 3, etc. This superscript is placed between the d and the y in numerator and after the dx in the denominator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The derivative of a function f of x or the derivative of y is written using prime which looks like an apostrophe and is written as a dot 3 which is the same as an apostrophe. The second derivative repeats the dot 3 for the second prime. For subsequent derivatives use the superscript indicator (dots 4-5) followed by the number representing the level of derivative. If anything follows this number other than a space, insert the baseline indicator (dot 5). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The empty set, or null set, can be written as a set of braces with a space between them or as a circle with a line through it. If writing it as a set of braces, the opening brace is dots 4-6 in front of the "of" contraction (dots 1-2-3-5-6). The closing brace is dots 4-6 in front of the "with" contraction (dots 2-3-4-5-6). If writing the empty set as a zero with a line through it, use a dot 4-5-6 in front of a zero (dots 3-5-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Enlarged braces are used when writing systems of equations, compound functions, or piecewise functions. To enlarge braces, just place a dot 6, as if it is capitalized, between the dots 4-6 and the opening or closing cell which are the same as the "of" (dots 1-2-3-5-6) or "with" (dots 2-3-4-5-6) contractions respectively. This set of three cells is written at the beginning and/or end of each line it pertains to. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Enlarged brackets are used when writing matrices. To enlarge brackets, just place a dot 6, as if it is capitalized, between the dot 4 and the opening or closing cell which are the same as the "of" (dots 1-2-3-5-6) or "with" (dots 2-3-4-5-6) contractions respectively. This set of three cells is written at the beginning and/or end of each line it pertains to. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Enlarged parentheses can be used in place of large brackets when writing matrices. To enlarge parentheses, just place a dot 6, as if it is capitalized, in front of both the open and closed parentheses. Remember the open and closed parentheses are the same as the "of" (dots 1-2-3-5-6) and "with" (dots 2-3-4-5-6) contractions respectively. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Enlarged vertical lines are used when writing determinants. To enlarge vertical lines, just place a dot 6, as if it is capitalized, before the vertical line "ou" (dots 2-3-5-6) contraction. This set of two cells is written at the beginning and end of each line it pertains to. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Epsilon is a Greek letter. The lowercase form of this letter is often used to represent an arbitrarily small positive quantity in calculus. To write Epsilon in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "e" (dots 1-5). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The five step rule is as follows. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified. If these are capital letters representing points, the capitalization indicator must be placed before each capitalized letter since each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction or the directly under indicator which is the "sh" contraction. Think "high" which uses the "gh" contraction or "shallow" which uses the "sh" contraction. Step 4: Write the modifier which is what is written directly over or under. Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Gamma is a Greek letter. The lowercase form of this letter is often used to represent an angle measure. To write Gamma in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "g" (dots 1-2-4-5). When writing this immediately after a trigonometric function such as sin, cos, tan, csc, sec, or cot, include a space before the Greek letter indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The Greek letters most commonly used as variables that represent angle measure are alpha, beta, gamma, theta, and phi. Pi is also used to represent a particular angle measures in radians. All of these letters are lowercase and have dots 4-6 in front of the letter(s) it represents. Alpha represents a, beta represents b, gamma represents g, theta represents th and uses the "th" contraction, phi represents f, and pi represents p. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Any letters of the Greek alphabet begin with dots 4-6 to identify it as a Greek letter. All lowercase letters begin with the dots 4-6 and are followed by the letter(s) it represents. All uppercase letters will still begin with the dots 4-6 followed by the capital indicator (dot 6) and then by the letter(s) it represents. The following Greek letters use a contraction to represent multiple letters: eta uses the contraction "wh" (dots 1-5-6), theta uses the contraction "th" (dots 1-4-5-6), and chi uses the contraction "and" (dots 1-2-3-4-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The indexed root, nth root, or indexed radical are used to indicate roots other than the square root (which is the same as the 2nd root.) The index is assumed to be two for a square root, but is explicitly stated for all other roots. For example, the index of the third root, also known as the cube root, is three. This index is placed between the "gh" contraction (dots 1-2-6) which is called the index-of-radical indicator and the "ar" contraction which is called the radical symbol. Then write what you are taking the root of without using any numeric indicators. Finally, finish or terminate the root with the "er" contraction which is called the termination indicator. Notice how the "er" contraction is used in the word terminate. If the problem has a nested radical or a radical inside of another radical, then a dots 4-6 is placed in front of the "gh" and "er" signs for the inner radical. Two dots 4-6 cells are placed in front of a 3rd level radical, three dots 4-6 cells are placed in front of a 4th level radical, etc. This should always be placed in front of both the "gh" and the "er" corresponding to that particular square root. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The infinity symbol is written using dot 6 followed by the full cell (dots 1-2-3-4-5-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The integer function is one of three types. The general integer function uses the opening bracket (dot 4, dots 1-2-3-5-6) followed by x and then a closing bracket (dot 4, dots 2-3-4-5-6). The greatest integer function, also known as the floor function, is represented with a special form of brackets that includes only the lower part of the bracket. The lower left bracket is dot 4, dots 5-6, dots 1-2-3-5-6 and the lower right bracket is dot 4, dots 5-6, dots 2-3-4-5-6. The least integer function, also known as the ceiling function, is represented with a special form of brackets that includes only the upper part of the bracket. The upper left bracket is dot 4, dots 4-5, dots 1-2-3-5-6 and the upper right bracket is dot 4, dots 4-5, dots 2-3-4-5-6. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The integral, or indefinite integral, starts with the integral sign which is dots 2-3-4-6. Then it is followed by the function and ends with dx. For the second integral or double integral, the integral sign is just repeated. The integral sign continues to be repeated for any subsequent integrals. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Lambda is a Greek letter. The lowercase form of this letter is often used to represent wavelength. To write Lambda in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "l" (dot 1-2-3). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Lines are denoted using the five step rule. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified which should be two capital letters. The capitalization indicator must be placed before each capitalized letter since each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction. Think "high" which also uses the "gh" contraction. Step 4: Write the modifier which is the two-way arrow symbol. It is the shape indicator (dots 1-2-4-6) followed by dots 2-4-6, dots 2-5, dots 2-5, dots 1-3-5. Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The different number systems are represented by uppercase letters. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Omega is a Greek letter. The lowercase form of this letter is often used to represent an angular velocity. To write Omega in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "w" (dots 2-4-5-6). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Parentheses are grouping symbols that have a beginning and an ending often called an opening and a closed parentheses. The opening parentheses is the beginning of the grouping and is the "of" contraction (dots 1-2-3-5-6) while the closing parentheses is the end of the grouping and is the "with" contraction (dots 2-3-4-5-6). The numeric indicator is not used inside grouping symbols such as parentheses. For parentheses that occur over more than one line, see enlarged parentheses. Note: Parentheses are always used when writing function notation which is written f(x) and read "f of x". Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The partial derivative, sometimes called the curly d, is often used in notation for calculus. To write this in Nemeth code, write dot 4 followed by the letter d (dots 1-4-5). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Permutations which are read n permutation r can be written several different ways. Method 1: capital p followed by n comma r inside a set of parentheses which are the "of" (dots 1-2-3-5-6) and "with" (dots 2-3-4-5-6) contractions. Method 2: capital p followed by the subscript indicator (dots 5-6) n comma r. Method 3: subscript indicator (dots 5-6) n capital p r. If r is a number, no subscript is needed before it, but if it is a variable, the subscript indicator is needed before it. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Phi is a Greek letter. The lowercase form of this letter is often used to represent an angle measure. To write Phi in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "f" (dot 1-2-4). When writing this immediately after a trigonometric function such as sin, cos, tan, csc, sec, or cot, include a space before the Greek letter indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Pi is a Greek letter. The lowercase form of this letter is often used to represent an angle measure in radians. It is also the ratio of the circumference of a circle to its diameter and is equal to approximately 3.14. To write Pi in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "p" (dots 1-2-3-4). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Prime can be used to represent feet or to represent the derivative of a function. Either way it is written using as a dot 3 which is the same as an apostrophe since it looks like an apostrophe in print. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Rational numbers (as fractions, mixed numbers, and decimals) are any numbers that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Examples and non-examples are given in a variety of ways in the sample documents. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Rays are denoted using the five step rule. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified which should be two capital letters. The capitalization indicator must be placed before each capitalized letter since each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction. Think "high" which also uses the "gh" contraction. Step 4: Write the modifier which is the right or left arrow symbol. It is the shape indicator (dots 1-2-4-6) followed by dots 2-5, dots 2-5, dots 1-3-5 for the right arrow or dots 2-4-6, dots 2-5, dots 2-5 for the left arrow. Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Segments are denoted using the five step rule. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified which should be two capital letters. The capitalization indicator must be placed before each capitalized letter since each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction. Think "high" which also uses the "gh" contraction. Step 4: Write the modifier which is the horizontal bar (dots 1-5-6). Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Sigma is a Greek letter. The lowercase form of this letter is often used to represent the standard deviation in statistics. To write Sigma in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the letter "s" (dots 2-3-4). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Sigma is a Greek letter. The uppercase form of this letter is often used to represent the summation operator for a series. To write Sigma in Nemeth code, begin with a Greek letter indicator (dots 4-6) followed by the capital indicator (dot 6) and then by the letter "s" (dots 2-3-4). Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Square root uses the "ar" contraction to start the square root and uses the "er" contraction to end or terminate the square root. Notice the "ar" contraction (dots 3-4-5) which is called the radical symbol is in the word "square" and the "er" contraction (dots 1-2-4-5-6) which is called the termination indicator is in the word terminate. If the problem has a nested square root or a square root inside of another square root, then a dots 4-6 is placed in front of the "ar" and "er" signs for the inner square root. Two dots 4-6 cells are placed in front of a 3rd level radical, three dots 4-6 cells are placed in front of a 4th level radical, etc. This should always be placed in front of both the "ar" and the "er" corresponding to that particular square root. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The subscript indicator (dots 5-6) is not always used to represent a subscript. It is not used when it follows a variable (letter) or a function name such as "log" and the subscript is a number. In these special cases, just write the letter immediately followed by the number with no numeric indicator. When this special case does not apply, use the subscript indicator before the subscript and the baseline indicator (dot 5) after the subscript. There is still no numeric indicator used within the subscript itself. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The superscript indicator (dots 4-5) is used to represent exponents, powers, or raised characters such as degree. It is used after the base and before the actual raised character or exponent. If something comes after the exponent other than a space, a baseline indicator (which is dot 5) must be used after the exponent. If a space comes after the exponent, no baseline indicator is needed. If an exponent is raised to another exponent, the superscript indicator is used twice instead of once before the second exponent. The same indicator is used to represent a raised number such as in the notation for an inverse function which is the letter f followed by the superscript indicator and then a negative one. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Theta is a Greek letter. The lowercase form of this letter is often used to represent an angle measure. To write Theta in Nemeth code, begin with a Greek letter indicator (dots 4-6) and then write the contraction "th" (dot 1-4-5-6). When writing this immediately after a trigonometric function such as sin, cos, tan, csc, sec, or cot, include a space before the Greek letter indicator. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

Vectors are denoted using the five step rule. Step 1: Begin with the multipurpose indicator (dot 5). Step 2: Write the expression being modified which should be two capital letters or one lowercase letter. If capital letters are used, the capitalization indicator must be placed before each capitalized letter since, in this case, each letter represents a separate point. Step 3: Write the directly over indicator which is the "gh" contraction. Think "high" which also uses the "gh" contraction. Step 4: Write the modifier which is the vector symbol. It is the shape indicator (dots 1-2-4-6) followed by dots 2-5, dots 2-5, dot 4, dots 1-3-5. Step 5: Write the termination indicator which is the "er" contraction (dots 1-2-4-5-6). Notice the "er" contraction in the word "termination." Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille

The vertical bar is the same as the "ou" contraction which is dots 1-2-5-6. Absolute Value is represented by a vertical bar on each side of a number or expression. Double or single vertical lines on each side of a vector are used to represent magnitude, length, or norm of vectors. A single vertical line is used to represent the words "such that," for example in set notation. The numeric indicator is not used inside grouping symbols such as the vertical bars representing absolute value. Samples in EBAE, Samples of Nemeth within UEB contexts, or Samples in print and SimBraille